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文档列表

11 General linear transformations in different bases/005 Linear transformations, Problem 4.mp4 817.9 MB
04 Coordinates, basis, and dimension/002 Bases in the 3-space, Problem 1.mp4 800.7 MB
05 Change of basis/010 Change of basis, Problem 1.mp4 676.4 MB
14 Eigenvalues and eigenvectors/013 Eigenvalues and eigenvectors, Problem 6.mp4 632.8 MB
11 General linear transformations in different bases/004 Linear transformations, Problem 3.mp4 621.8 MB
15 Diagonalization/009 Eigenspaces, Problem 2.mp4 613.4 MB
03 Linear combinations and linear independence/006 Linear combinations, Problem 2.mp4 586.2 MB
14 Eigenvalues and eigenvectors/010 Eigenvalues and eigenvectors, Problem 3.mp4 582.3 MB
04 Coordinates, basis, and dimension/006 Bases in the 4-space, Problem 4.mp4 575.3 MB
11 General linear transformations in different bases/002 Linear transformations, Problem 1.mp4 560.6 MB
14 Eigenvalues and eigenvectors/009 Eigenvalues and eigenvectors for examples from Video 180.mp4 548.3 MB
12 Gram-Schmidt process/007 Coordinates in ON bases, Problem 1.mp4 494.0 MB
09 Geometry of matrix transformations on R^2 and R^3/013 Rotations in the 3-space, Problem 7.mp4 485.3 MB
15 Diagonalization/010 Eigenvectors corresponding to different eigenvalues are linearly independent.mp4 481.2 MB
05 Change of basis/012 Change of basis, Problem 3.mp4 477.3 MB
03 Linear combinations and linear independence/015 Linearly independent generators, Problem 6.mp4 466.1 MB
10 Properties of matrix transformations/011 Compositions of linear transformations, Problem 5.mp4 463.0 MB
11 General linear transformations in different bases/009 Linear transformations in different bases, Problem 7.mp4 456.1 MB
14 Eigenvalues and eigenvectors/012 Eigenvalues and eigenvectors, Problem 5.mp4 422.6 MB
11 General linear transformations in different bases/003 Linear transformations, Problem 2.mp4 422.4 MB
02 Real vector spaces and their subspaces/015 Subspaces, Problem 2.mp4 407.1 MB
12 Gram-Schmidt process/010 Coordinates in orthogonal bases, Problem 2.mp4 399.0 MB
09 Geometry of matrix transformations on R^2 and R^3/012 Projection on a given plane, Problem 6.mp4 384.3 MB
13 Orthogonal matrices/010 Property 5_ Preserving distances and angles.mp4 383.9 MB
02 Real vector spaces and their subspaces/016 Subspaces, Problem 3.mp4 380.6 MB
06 Row space, column space, and nullspace of a matrix/014 Nullspace, Problem 10.mp4 379.9 MB
06 Row space, column space, and nullspace of a matrix/013 Nullspace, Problem 9.mp4 372.3 MB
04 Coordinates, basis, and dimension/005 Bases in the 4-space, Problem 3.mp4 369.9 MB
03 Linear combinations and linear independence/019 Linear independence in C^∞(R), Problem 9.mp4 364.9 MB
08 Matrix transformations from R^n to R^m/009 Image, kernel, and inverse operators, Problem 2.mp4 361.4 MB
11 General linear transformations in different bases/006 Linear transformations, Problem 5.mp4 360.6 MB
09 Geometry of matrix transformations on R^2 and R^3/004 Projection on a given vector, Problem 1.mp4 357.8 MB
06 Row space, column space, and nullspace of a matrix/010 A basis in the space of polynomials, Problem 7.mp4 344.8 MB
08 Matrix transformations from R^n to R^m/013 Inverse operators, Problem 6.mp4 343.2 MB
14 Eigenvalues and eigenvectors/007 How to compute eigenvectors.mp4 335.3 MB
11 General linear transformations in different bases/007 Linear transformations in different bases, Problem 6.mp4 332.2 MB
12 Gram-Schmidt process/013 Projection Theorem 2.mp4 326.1 MB
03 Linear combinations and linear independence/008 Span, Problem 3.mp4 319.2 MB
03 Linear combinations and linear independence/009 Span, Problem 4.mp4 315.9 MB
06 Row space, column space, and nullspace of a matrix/008 Determining a basis for a span consisting of a subset of given vectors, Prob.mp4 313.8 MB
03 Linear combinations and linear independence/016 Linear independence in the set of matrices, Problem 7.mp4 310.3 MB
11 General linear transformations in different bases/010 Linear transformations in different bases, Problem 8.mp4 308.8 MB
10 Properties of matrix transformations/010 Compositions of linear transformations, Problem 4.mp4 305.5 MB
12 Gram-Schmidt process/020 Gram-Schmidt Process, Problem 7.mp4 298.9 MB
11 General linear transformations in different bases/013 Linear transformations, Problem 11.mp4 296.4 MB
06 Row space, column space, and nullspace of a matrix/007 Determining a basis for a span consisting of a subset of given vectors, Prob.mp4 293.6 MB
09 Geometry of matrix transformations on R^2 and R^3/011 Symmetry about a given plane, Problem 5.mp4 287.3 MB
05 Change of basis/011 Change of basis, Problem 2.mp4 286.3 MB
03 Linear combinations and linear independence/005 Linear combinations, Problem 1.mp4 283.4 MB
06 Row space, column space, and nullspace of a matrix/003 What are the elementary row operations doing to the row spaces_.mp4 275.9 MB
15 Diagonalization/013 Diagonalizability, Problem 3.mp4 270.2 MB
11 General linear transformations in different bases/011 Linear transformations in different bases, Problem 9.mp4 264.2 MB
06 Row space, column space, and nullspace of a matrix/006 Determining a basis for a span, Problem 3.mp4 262.9 MB
15 Diagonalization/017 Diagonalizability, Problem 7.mp4 262.7 MB
13 Orthogonal matrices/012 Orthogonal matrices, Problem 1.mp4 262.2 MB
14 Eigenvalues and eigenvectors/011 Eigenvalues and eigenvectors, Problem 4.mp4 260.3 MB
09 Geometry of matrix transformations on R^2 and R^3/009 Plane symmetry in the 3-space, Problem 3.mp4 259.9 MB
08 Matrix transformations from R^n to R^m/005 When is a function from Rn to Rm linear_ Approach 2.mp4 259.3 MB
05 Change of basis/014 Change of basis, Problem 5.mp4 251.2 MB
10 Properties of matrix transformations/004 Transformations of straight lines, Problem 2.mp4 245.0 MB
12 Gram-Schmidt process/015 Calculating projections, Problem 4.mp4 244.1 MB
02 Real vector spaces and their subspaces/010 Some properties of vector spaces.mp4 242.7 MB
02 Real vector spaces and their subspaces/009 Two properties of vector spaces; Definition of difference.mp4 237.8 MB
02 Real vector spaces and their subspaces/011 What is a subspace.mp4 226.2 MB
04 Coordinates, basis, and dimension/011 Dimension of a subspace, Problem 6.mp4 223.7 MB
06 Row space, column space, and nullspace of a matrix/009 A tricky one_ Let rows become columns, Problem 6.mp4 223.2 MB
02 Real vector spaces and their subspaces/007 Vector spaces, Example 4_ complex numbers.mp4 220.2 MB
08 Matrix transformations from R^n to R^m/012 Image and kernel, Problem 5.mp4 213.8 MB
06 Row space, column space, and nullspace of a matrix/005 Column space, Problem 2.mp4 210.2 MB
02 Real vector spaces and their subspaces/004 Formal definition of vector spaces Example 1_ Rn.mp4 208.7 MB
12 Gram-Schmidt process/019 Gram-Schmidt Process, Problem 6.mp4 208.1 MB
08 Matrix transformations from R^n to R^m/014 Linear transformations, Problem 7.mp4 205.7 MB
04 Coordinates, basis, and dimension/012 Bases in a space of functions, Problem 7.mp4 205.6 MB
08 Matrix transformations from R^n to R^m/016 Linear transformations, Problem 9.mp4 202.9 MB
02 Real vector spaces and their subspaces/006 Vector spaces, Example 3_ real-valued functions on some interval.mp4 199.7 MB
09 Geometry of matrix transformations on R^2 and R^3/005 Symmetry about the line y = kx, Problem 2.mp4 197.8 MB
10 Properties of matrix transformations/009 Why does it work_.mp4 195.9 MB
08 Matrix transformations from R^n to R^m/011 Kernel, Problem 4.mp4 190.0 MB
09 Geometry of matrix transformations on R^2 and R^3/002 An example with nontrivial kernel.mp4 187.8 MB
03 Linear combinations and linear independence/017 Linear independence in C^0[−∞, ∞], Problem 8.mp4 186.9 MB
07 Rank, nullity, and four fundamental matrix spaces/004 Relationship between rank and nullity, Problem 1.mp4 182.9 MB
03 Linear combinations and linear independence/022 Linear independence in C^∞(R), Problem 11.mp4 177.2 MB
08 Matrix transformations from R^n to R^m/015 Kernel and geometry, Problem 8.mp4 176.5 MB
05 Change of basis/013 Change of basis, Problem 4.mp4 175.9 MB
06 Row space, column space, and nullspace of a matrix/011 Nullspace for a matrix.mp4 175.1 MB
15 Diagonalization/019 Powers of matrices, Problem 8.mp4 173.0 MB
12 Gram-Schmidt process/012 Projection Theorem 1.mp4 169.9 MB
13 Orthogonal matrices/013 Orthogonal matrices, Problem 2.mp4 168.7 MB
09 Geometry of matrix transformations on R^2 and R^3/010 Projections on planes in the 3-space, Problem 4.mp4 165.1 MB
01 Introduction to the course/001 Introduction to the course.mp4 164.7 MB
08 Matrix transformations from R^n to R^m/010 Basis for the image, Problem 3.mp4 163.7 MB
02 Real vector spaces and their subspaces/017 Subspaces, Problem 4.mp4 152.8 MB
12 Gram-Schmidt process/011 Orthonormal bases, Problem 3.mp4 150.1 MB
11 General linear transformations in different bases/012 Linear transformations, Problem 10.mp4 148.1 MB
12 Gram-Schmidt process/016 Calculating projections, Problem 5.mp4 144.3 MB
09 Geometry of matrix transformations on R^2 and R^3/003 Line symmetries in the plane.mp4 139.0 MB
09 Geometry of matrix transformations on R^2 and R^3/006 Rotation by 90 degrees about the origin.mp4 138.7 MB
10 Properties of matrix transformations/005 Change of area (volume) under linear operators in the plane (space).mp4 135.6 MB
09 Geometry of matrix transformations on R^2 and R^3/001 Our unifying example_ linear transformations and change of basis.mp4 134.9 MB
13 Orthogonal matrices/005 Useful formulas for the coming proofs.mp4 134.6 MB
13 Orthogonal matrices/011 Property 6_ Product of orthogonal matrices is orthogonal.mp4 134.2 MB
04 Coordinates, basis, and dimension/009 Coordinates with respect to a basis are unique.mp4 128.6 MB
15 Diagonalization/020 Diagonalization, Problem 9.mp4 126.6 MB
07 Rank, nullity, and four fundamental matrix spaces/003 Relationship between rank and nullity.mp4 122.0 MB
13 Orthogonal matrices/004 A 3-by-3 example.mp4 113.8 MB
04 Coordinates, basis, and dimension/004 Bases in the 3-space, Problem 2.mp4 112.4 MB
03 Linear combinations and linear independence/021 Linear independence in C^∞(R), Problem 10.mp4 111.5 MB
15 Diagonalization/008 Eigenspaces; geometric and algebraic multiplicity of eigenvalues.mp4 108.8 MB
13 Orthogonal matrices/007 Property 2_ Each orthogonal matrix A is invertible and A−1 is also orthogona.mp4 104.3 MB
08 Matrix transformations from R^n to R^m/008 Matrix transformations, Problem 1.mp4 103.6 MB
05 Change of basis/009 How to recalculate coordinates between two non-standard bases_ An algorithm.mp4 103.2 MB
14 Eigenvalues and eigenvectors/001 Crash course in factoring polynomials.mp4 101.9 MB
07 Rank, nullity, and four fundamental matrix spaces/007 Orthogonal complements, Problem 4.mp4 101.9 MB
14 Eigenvalues and eigenvectors/004 Eigenvalues and eigenvectors geometrically.mp4 100.1 MB
02 Real vector spaces and their subspaces/008 Cancellation property.mp4 97.8 MB
10 Properties of matrix transformations/003 Parallel lines transform into parallel lines, Problem 1.mp4 97.1 MB
03 Linear combinations and linear independence/018 Vandermonde determinant and polynomials.mp4 96.9 MB
14 Eigenvalues and eigenvectors/005 Eigenvalues and eigenvectors, Problem 1.mp4 95.7 MB
02 Real vector spaces and their subspaces/005 Vector spaces, Example 2_ m × n matrices with real entries.mp4 95.7 MB
12 Gram-Schmidt process/001 Dot product and orthogonality until now.mp4 95.5 MB
15 Diagonalization/015 Diagonalizability, Problem 5.mp4 94.4 MB
04 Coordinates, basis, and dimension/007 Bases in the space of polynomials, Problem 5.mp4 93.2 MB
04 Coordinates, basis, and dimension/003 Bases in the plane and in the 3-space.mp4 93.1 MB
14 Eigenvalues and eigenvectors/006 How to compute eigenvalues Characteristic polynomial.mp4 89.6 MB
10 Properties of matrix transformations/008 How to obtain the standard matrix of a composition of linear transformations.mp4 89.4 MB
05 Change of basis/008 Two non-standard bases, Method 2.mp4 88.4 MB
15 Diagonalization/003 Similarity of matrices is an equivalence relation (RST).mp4 84.5 MB
08 Matrix transformations from R^n to R^m/001 What do we mean by linear_.mp4 83.0 MB
06 Row space, column space, and nullspace of a matrix/001 What you are going to learn in this section.mp4 81.2 MB
09 Geometry of matrix transformations on R^2 and R^3/008 Expansion, compression, scaling, and shear.mp4 80.9 MB
03 Linear combinations and linear independence/012 Linear independence and linear dependence.mp4 79.2 MB
02 Real vector spaces and their subspaces/012 All the subspaces in R2.mp4 79.1 MB
04 Coordinates, basis, and dimension/008 Coordinates with respect to a basis.mp4 77.8 MB
10 Properties of matrix transformations/007 Compositions of linear transformations.mp4 77.7 MB
08 Matrix transformations from R^n to R^m/006 When is a function from Rn to Rm linear_ Approach 3.mp4 77.6 MB
07 Rank, nullity, and four fundamental matrix spaces/009 The Fundamental Theorem of Linear Algebra and Gilbert Strang.mp4 77.1 MB
05 Change of basis/003 Transition matrix, a derivation.mp4 76.9 MB
08 Matrix transformations from R^n to R^m/003 How to think about functions from Rn to Rm_.mp4 74.7 MB
03 Linear combinations and linear independence/002 Linear combinations in Part 1.mp4 74.6 MB
15 Diagonalization/006 How to diagonalize a matrix, a recipe.mp4 74.5 MB
12 Gram-Schmidt process/017 Gram-Schmidt Process.mp4 74.4 MB
03 Linear combinations and linear independence/014 An important remark on linear independence in Rn.mp4 74.3 MB
12 Gram-Schmidt process/009 Each orthogonal set is linearly independent, Proof.mp4 72.6 MB
05 Change of basis/002 It is easy to recalculate from the standard basis.mp4 72.5 MB
05 Change of basis/015 Change to an orthonormal basis in R^2.mp4 69.8 MB
05 Change of basis/005 Our unifying example.mp4 69.8 MB
08 Matrix transformations from R^n to R^m/004 When is a function from Rn to Rm linear_ Approach 1.mp4 69.6 MB
03 Linear combinations and linear independence/013 Geometry of linear independence and linear dependence.mp4 68.7 MB
03 Linear combinations and linear independence/001 Our unifying example.mp4 68.3 MB
08 Matrix transformations from R^n to R^m/002 Some terminology.mp4 68.2 MB
15 Diagonalization/014 Diagonalizability, Problem 4.mp4 66.8 MB
06 Row space, column space, and nullspace of a matrix/004 What are the elementary row operations doing to the column spaces_.mp4 64.3 MB
11 General linear transformations in different bases/001 Linear transformations between two linear spaces.mp4 64.2 MB
11 General linear transformations in different bases/008 Linear transformations in different bases.mp4 63.8 MB
02 Real vector spaces and their subspaces/003 Our prototype.mp4 63.4 MB
08 Matrix transformations from R^n to R^m/007 Approaches 2 and 3 are equivalent.mp4 63.2 MB
07 Rank, nullity, and four fundamental matrix spaces/005 Relationship between rank and nullity, Problem 2.mp4 62.6 MB
15 Diagonalization/016 Diagonalizability, Problem 6.mp4 61.6 MB
06 Row space, column space, and nullspace of a matrix/012 How to find the nullspace, Problem 8.mp4 59.9 MB
09 Geometry of matrix transformations on R^2 and R^3/007 Rotation by the angle α about the origin.mp4 59.7 MB
12 Gram-Schmidt process/002 Orthonormal bases are awesome.mp4 59.5 MB
03 Linear combinations and linear independence/011 What do we mean by trivial_.mp4 58.6 MB
10 Properties of matrix transformations/006 Change of area under linear transformations, Problem 3.mp4 58.3 MB
14 Eigenvalues and eigenvectors/014 Eigenvalues and eigenvectors, Problem 7.mp4 57.6 MB
15 Diagonalization/012 Necessary and sufficient condition for diagonalizability.mp4 57.4 MB
06 Row space, column space, and nullspace of a matrix/002 Row space and column space for a matrix.mp4 56.9 MB
16 Wrap-up Linear Algebra and Geometry 2/001 Linear Algebra and Geometry 2, Wrap-up.mp4 56.2 MB
04 Coordinates, basis, and dimension/001 What is a basis and dimension_.mp4 54.9 MB
03 Linear combinations and linear independence/020 Wronskian and linear independence in C∞(R).mp4 53.0 MB
12 Gram-Schmidt process/008 Coordinates in orthogonal bases, Theorem and proof.mp4 52.8 MB
03 Linear combinations and linear independence/007 What is a span, definition and some examples.mp4 52.5 MB
05 Change of basis/007 Two non-standard bases, Method 1.mp4 52.1 MB
02 Real vector spaces and their subspaces/014 Subspaces, Problem 1.mp4 50.9 MB
05 Change of basis/001 Coordinates in different bases.mp4 49.0 MB
13 Orthogonal matrices/001 Product of a matrix and its transposed is symmetric.mp4 46.9 MB
15 Diagonalization/001 Why you should love diagonal matrices.mp4 44.5 MB
14 Eigenvalues and eigenvectors/008 Finding eigenvalues and eigenvectors_ short and sweet.mp4 44.1 MB
02 Real vector spaces and their subspaces/013 All the subspaces in R3.mp4 43.4 MB
15 Diagonalization/004 Shared properties of similar matrices.mp4 42.9 MB
12 Gram-Schmidt process/014 Projection Formula, an illustration in the 3-space.mp4 42.4 MB
13 Orthogonal matrices/003 Geometry of 2-by-2 orthogonal matrices.mp4 41.9 MB
12 Gram-Schmidt process/018 Gram-Schmidt Process, Our unifying example.mp4 41.7 MB
10 Properties of matrix transformations/002 What happens with vector subspaces and affine subspaces under linear transfo.mp4 40.4 MB
13 Orthogonal matrices/009 Property 4_ Orthogonal matrices are transition matrices between ON-bases.mp4 39.8 MB
03 Linear combinations and linear independence/003 Linear combinations, new stuff. Example 1.mp4 38.4 MB
15 Diagonalization/007 Diagonalize our favourite matrix.mp4 38.3 MB
07 Rank, nullity, and four fundamental matrix spaces/008 Four fundamental matrix spaces.mp4 38.2 MB
07 Rank, nullity, and four fundamental matrix spaces/001 Rank of a matrix.mp4 38.1 MB
13 Orthogonal matrices/002 Definition and examples of orthogonal matrices.mp4 37.5 MB
13 Orthogonal matrices/006 Property 1_ Determinant of each orthogonal matrix is 1 or −1.mp4 36.8 MB
01 Introduction to the course/001 Slides Introduction to the course.pdf 36.6 MB
02 Real vector spaces and their subspaces/001 From abstract to concrete.mp4 35.6 MB
04 Coordinates, basis, and dimension/010 Coordinates in our unifying example.mp4 35.6 MB
10 Properties of matrix transformations/001 What kind of properties we will discuss.mp4 35.3 MB
03 Linear combinations and linear independence/010 Span, Problem 5.mp4 34.7 MB
13 Orthogonal matrices/008 Property 3_ Orthonormal columns and rows.mp4 34.5 MB
12 Gram-Schmidt process/006 Orthonormal bases are awesome, Reason 4_ coordinates.mp4 34.1 MB
05 Change of basis/004 Previous example with transition matrix.mp4 33.1 MB
15 Diagonalization/021 Sneak peek into the next course; orthogonal diagonalization.mp4 30.9 MB
02 Real vector spaces and their subspaces/002 From concrete to abstract.mp4 30.1 MB
14 Eigenvalues and eigenvectors/002 Eigenvalues and eigenvectors, the terms.mp4 29.6 MB
03 Linear combinations and linear independence/004 Linear combinations Example 2.mp4 28.6 MB
15 Diagonalization/018 Powers of matrices.mp4 26.8 MB
12 Gram-Schmidt process/005 Orthonormal bases are awesome, Reason 3_ transition matrix.mp4 26.0 MB
15 Diagonalization/005 Diagonalizable matrices.mp4 25.8 MB
05 Change of basis/006 One more simple example and bases.mp4 25.2 MB
07 Rank, nullity, and four fundamental matrix spaces/002 Nullity.mp4 25.2 MB
16 Wrap-up Linear Algebra and Geometry 2/002 Yes, there will be Part 3!.mp4 24.9 MB
15 Diagonalization/011 A sufficient, but not necessary, condition for diagonalizability.mp4 23.4 MB
12 Gram-Schmidt process/004 Orthonormal bases are awesome, Reason 2_ dot product.mp4 21.9 MB
12 Gram-Schmidt process/003 Orthonormal bases are awesome, Reason 1_ distance.mp4 19.7 MB
15 Diagonalization/002 Similar matrices.mp4 19.0 MB
07 Rank, nullity, and four fundamental matrix spaces/006 Relationship between rank and nullity, Problem 3.mp4 15.7 MB
16 Wrap-up Linear Algebra and Geometry 2/003 Final words.mp4 15.6 MB
16 Wrap-up Linear Algebra and Geometry 2/212 Slides Linear Algebra and Geometry 2 Wrap-up.pdf 14.3 MB
14 Eigenvalues and eigenvectors/003 Order of defining, order of computing.mp4 13.9 MB
04 Coordinates, basis, and dimension/043 Slides Bases in the plane and in the 3 space.pdf 9.7 MB
05 Change of basis/061 Slides How to recalculate coordinates between two non-standard bases An algorithm.pdf 6.6 MB
03 Linear combinations and linear independence/019 Slides Our unifying example.pdf 6.5 MB
05 Change of basis/060 Slides Two non standard bases Method 2.pdf 6.0 MB
14 Eigenvalues and eigenvectors/185 Slides Eigenvalues and eigenvectors for examples from Video 180.pdf 5.5 MB
10 Properties of matrix transformations/124 Slides Change of area and volume under linear operators in the plane and space.pdf 5.3 MB
15 Diagonalization/211 Slides Sneak peek into the next course Orthogonal diagonalization.pdf 5.1 MB
12 Gram-Schmidt process/144 Slides Dot product and orthogonality until now.pdf 4.8 MB
14 Eigenvalues and eigenvectors/180 Slides Eigenvalues and eigenvectors geometrically.pdf 4.7 MB
03 Linear combinations and linear independence/020 Slides Linear combinations In Part 1.pdf 4.7 MB
03 Linear combinations and linear independence/031 Slides Geometry of linear independence and linear dependence.pdf 4.2 MB
05 Change of basis/067 Slides Change to an orthonormal basis in the plane.pdf 4.1 MB
13 Orthogonal matrices/166 Slides Geometry of 2 by 2 orthogonal matrices.pdf 3.7 MB
14 Eigenvalues and eigenvectors/190 Slides Eigenvalues and eigenvectors Problem 7.pdf 3.6 MB
11 General linear transformations in different bases/135 Notes Linear transformations Problem 4.pdf 3.6 MB
14 Eigenvalues and eigenvectors/185 Notes Eigenvalues and eigenvectors for examples from Video 180.pdf 3.5 MB
09 Geometry of matrix transformations on R^2 and R^3/109 Slides Line symmetries in the plane.pdf 3.5 MB
04 Coordinates, basis, and dimension/042 Notes Bases in the 3 space Problem 1.pdf 3.4 MB
13 Orthogonal matrices/165 Slides Definition and examples of orthogonal matrices.pdf 3.2 MB
15 Diagonalization/200 Notes Eigenvectors corresponding to different eigenvalues are linearly independent.pdf 3.2 MB
15 Diagonalization/197 Slides Diagonalize our favorite matrix.pdf 3.1 MB
09 Geometry of matrix transformations on R^2 and R^3/107 Slides Our unifying example Linear transformations and change of basis.pdf 2.8 MB
02 Real vector spaces and their subspaces/016 Notes Subspace Problem 2.pdf 2.8 MB
12 Gram-Schmidt process/150 Notes Coordinates in ON bases Problem 1.pdf 2.6 MB
15 Diagonalization/199 Notes Eigenspaces Problem 2.pdf 2.6 MB
05 Change of basis/062 Notes Change of basis Problem 1.pdf 2.6 MB
14 Eigenvalues and eigenvectors/189 Notes Eigenvalues and eigenvectors Problem 6.pdf 2.6 MB
11 General linear transformations in different bases/133 Notes Linear transformations Problem 2.pdf 2.5 MB
03 Linear combinations and linear independence/024 Notes Linear combinations Problem 2.pdf 2.4 MB
02 Real vector spaces and their subspaces/017 Notes Subspace Problem 3.pdf 2.4 MB
11 General linear transformations in different bases/134 Notes Linear transformations Problem 3.pdf 2.4 MB
06 Row space, column space, and nullspace of a matrix/072 Notes Column space Problem 2.pdf 2.4 MB
13 Orthogonal matrices/173 Notes Property 5 Preserving distances and angles.pdf 2.4 MB
04 Coordinates, basis, and dimension/046 Notes Bases in the 4 space Problem 4.pdf 2.3 MB
08 Matrix transformations from R^n to R^m/097 Slides Approaches 2 and 3 are equivalent.pdf 2.3 MB
15 Diagonalization/205 Slides Diagonalizability Problem 5.pdf 2.2 MB
09 Geometry of matrix transformations on R^2 and R^3/114 Slides Expansion Compression Scaling and Shear.pdf 2.2 MB
05 Change of basis/058 Slides One more simple example.pdf 2.2 MB
14 Eigenvalues and eigenvectors/182 Slides How to compute eigenvalues Characteristic polynomial.pdf 2.1 MB
05 Change of basis/064 Notes Change of basis Problem 3.pdf 2.0 MB
14 Eigenvalues and eigenvectors/186 Notes Eigenvalues and eigenvectors Problem 3.pdf 2.0 MB
12 Gram-Schmidt process/156 Notes Projection Theorem 2.pdf 2.0 MB
11 General linear transformations in different bases/132 Notes Linear transformations Problem 1.pdf 2.0 MB
04 Coordinates, basis, and dimension/045 Notes Bases in the 4 space Problem 3.pdf 2.0 MB
06 Row space, column space, and nullspace of a matrix/071 Slides What are the elementary row operations doing to the column spaces.pdf 2.0 MB
14 Eigenvalues and eigenvectors/183 Slides How to compute eigenvectors.pdf 1.9 MB
10 Properties of matrix transformations/128 Slides Why does it work.pdf 1.9 MB
09 Geometry of matrix transformations on R^2 and R^3/113 Slides Rotation by the angle alpha about the origin.pdf 1.9 MB
09 Geometry of matrix transformations on R^2 and R^3/118 Notes Projection on a given plane Problem 6.pdf 1.9 MB
14 Eigenvalues and eigenvectors/177 Slides Crash course in factoring polynomials.pdf 1.9 MB
12 Gram-Schmidt process/153 Notes Coordinates in orthogonal bases Problem 2.pdf 1.8 MB
14 Eigenvalues and eigenvectors/188 Notes Eigenvalues and eigenvectors Problem 5.pdf 1.8 MB
03 Linear combinations and linear independence/030 Slides Linear independence and linear dependence.pdf 1.8 MB
09 Geometry of matrix transformations on R^2 and R^3/112 Slides Rotation by 90 degrees about the origin.pdf 1.8 MB
13 Orthogonal matrices/172 Slides Property 4 Orthogonal matrices are transition matrices between ON-bases.pdf 1.7 MB
10 Properties of matrix transformations/127 Slides How to obtain the standard matrix of a composition of linear transformations.pdf 1.7 MB
09 Geometry of matrix transformations on R^2 and R^3/117 Slides Symmetry about a given plane Problem 5.pdf 1.7 MB
07 Rank, nullity, and four fundamental matrix spaces/088 Slides Orthogonal complements Problem 4.pdf 1.7 MB
09 Geometry of matrix transformations on R^2 and R^3/118 Slides Projection on a given plane Problem 6.pdf 1.7 MB
09 Geometry of matrix transformations on R^2 and R^3/119 Notes Rotations in the 3-space Problem 7.pdf 1.7 MB
11 General linear transformations in different bases/131 Slides Linear transformations between two linear spaces.pdf 1.6 MB
09 Geometry of matrix transformations on R^2 and R^3/110 Slides Projection on a given vector Problem 1.pdf 1.6 MB
15 Diagonalization/202 Slides Necessary and sufficient condition for diagonalizability.pdf 1.6 MB
12 Gram-Schmidt process/161 Slides Gram Schmidt Process Our unifying example.pdf 1.6 MB
03 Linear combinations and linear independence/036 Slides Vandermonde determinant and polynomials.pdf 1.6 MB
12 Gram-Schmidt process/163 Notes Gram Schmidt Process Problem 7.pdf 1.6 MB
02 Real vector spaces and their subspaces/008 Notes Vector spaces Example 4 Complex numbers.pdf 1.6 MB
02 Real vector spaces and their subspaces/007 Slides Vector spaces Example 3 Functions.pdf 1.6 MB
09 Geometry of matrix transformations on R^2 and R^3/111 Slides Symmetry about a line Problem 2.pdf 1.5 MB
10 Properties of matrix transformations/122 Slides Parallel lines transform into parallel lines Problem 1.pdf 1.5 MB
10 Properties of matrix transformations/130 Notes Compositions of linear transformations Problem 5.pdf 1.5 MB
08 Matrix transformations from R^n to R^m/099 Slides Image, kernel, and inverse operators Problem 2.pdf 1.5 MB
07 Rank, nullity, and four fundamental matrix spaces/090 Slides The Fundamental Theorem of Linear Algebra and Gilbert Strang.pdf 1.5 MB
02 Real vector spaces and their subspaces/010 Notes Two properties of vector spaces Definition of difference.pdf 1.5 MB
08 Matrix transformations from R^n to R^m/103 Notes Inverse operators Problem 6.pdf 1.5 MB
10 Properties of matrix transformations/125 Slides Change of area under linear operators in the plane Problem 3.pdf 1.5 MB
15 Diagonalization/193 Slides Similarity of matrices is an equivalence relation RST.pdf 1.5 MB
11 General linear transformations in different bases/136 Notes Linear transformations Problem 5.pdf 1.5 MB
07 Rank, nullity, and four fundamental matrix spaces/084 Slides Relationship between the rank and nullity.pdf 1.5 MB
11 General linear transformations in different bases/143 Notes Linear transformations Problem 11.pdf 1.5 MB
05 Change of basis/063 Notes Change of basis Problem 2.pdf 1.5 MB
03 Linear combinations and linear independence/027 Notes Span Problem 4.pdf 1.5 MB
03 Linear combinations and linear independence/033 Notes Linearly independent generators Problem 6.pdf 1.4 MB
11 General linear transformations in different bases/139 Notes Linear transformations in different bases Problem 7.pdf 1.4 MB
07 Rank, nullity, and four fundamental matrix spaces/089 Slides Four fundamental matrix spaces.pdf 1.4 MB
02 Real vector spaces and their subspaces/013 Slides All the subspace in R2.pdf 1.4 MB
15 Diagonalization/196 Slides How to diagonalize a matrix A recipe.pdf 1.3 MB
02 Real vector spaces and their subspaces/011 Notes Some properties of vector spaces.pdf 1.3 MB
15 Diagonalization/194 Slides Shared properties of similar matrices.pdf 1.3 MB
06 Row space, column space, and nullspace of a matrix/077 Notes A basis in the space of polynomials Problem 7.pdf 1.3 MB
02 Real vector spaces and their subspaces/012 Notes What is a subspace.pdf 1.3 MB
03 Linear combinations and linear independence/025 Slides What is span Definition and some examples.pdf 1.3 MB
02 Real vector spaces and their subspaces/006 Slides Vector spaces Example 2 Matrices.pdf 1.3 MB
06 Row space, column space, and nullspace of a matrix/070 Notes What are the elementary row operations doing to the row spaces.pdf 1.3 MB
03 Linear combinations and linear independence/026 Notes Span Problem 3.pdf 1.3 MB
04 Coordinates, basis, and dimension/051 Notes Dimension of a subspace Problem 6.pdf 1.3 MB
11 General linear transformations in different bases/140 Notes Linear transformations in different bases Problem 8.pdf 1.3 MB
03 Linear combinations and linear independence/034 Notes Linear independence in the set of matrices Problem 7.pdf 1.3 MB
02 Real vector spaces and their subspaces/007 Notes Vector spaces Example 3 Functions.pdf 1.2 MB
12 Gram-Schmidt process/155 Slides Projection Theorem 1.pdf 1.2 MB
05 Change of basis/066 Notes Change of basis Problem 5.pdf 1.2 MB
06 Row space, column space, and nullspace of a matrix/070 Slides What are the elementary row operations doing to the row spaces.pdf 1.2 MB
15 Diagonalization/206 Slides Diagonalizability Problem 6.pdf 1.2 MB
05 Change of basis/054 Slides It is easy to recalculate from the standard basis.pdf 1.2 MB
09 Geometry of matrix transformations on R^2 and R^3/110 Notes Projection on a given vector Problem 1.pdf 1.2 MB
14 Eigenvalues and eigenvectors/187 Notes Eigenvalues and eigenvectors Problem 4.pdf 1.2 MB
10 Properties of matrix transformations/129 Notes Compositions of linear transformations Problem 4.pdf 1.2 MB
05 Change of basis/055 Slides Transition matrix A derivation.pdf 1.2 MB
03 Linear combinations and linear independence/023 Notes Linear combinations Problem 1.pdf 1.2 MB
14 Eigenvalues and eigenvectors/183 Notes How to compute eigenvectors.pdf 1.2 MB
08 Matrix transformations from R^n to R^m/099 Notes Image, kernel, and inverse operators Problem 2.pdf 1.2 MB
09 Geometry of matrix transformations on R^2 and R^3/117 Notes Symmetry about a given plane Problem 5.pdf 1.2 MB
13 Orthogonal matrices/175 Notes Orthogonal matrices Problem 1.pdf 1.2 MB
08 Matrix transformations from R^n to R^m/102 Notes Image and kernel Problem 5.pdf 1.1 MB
15 Diagonalization/204 Slides Diagonalizability Problem 4.pdf 1.1 MB
06 Row space, column space, and nullspace of a matrix/074 Notes Determining a basis for a span consisting of a subset of given vectors Problem 4.pdf 1.1 MB
04 Coordinates, basis, and dimension/050 Slides Coordinates in our unifying example.pdf 1.1 MB
10 Properties of matrix transformations/128 Notes Why does it work.pdf 1.1 MB
11 General linear transformations in different bases/141 Notes Linear transformations in different bases Problem 9.pdf 1.1 MB
13 Orthogonal matrices/169 Slides Property 1 Determinant of each orthogonal matrix is 1 or -1.pdf 1.1 MB
15 Diagonalization/195 Slides Diagonalizable matrices.pdf 1.1 MB
15 Diagonalization/207 Notes Diagonalizability Problem 7.pdf 1.1 MB
11 General linear transformations in different bases/137 Notes Linear transformations Problem 6.pdf 1.1 MB
06 Row space, column space, and nullspace of a matrix/080 Notes Nullspace Problem 9.pdf 1.1 MB
12 Gram-Schmidt process/162 Notes Gram Schmidt Process Problem 6.pdf 1.1 MB
05 Change of basis/059 Slides Two non standard bases Method 1.pdf 1.1 MB
15 Diagonalization/203 Notes Diagonalizability Problem 3.pdf 1.1 MB
06 Row space, column space, and nullspace of a matrix/081 Notes Nullspace Problem 10.pdf 1.1 MB
12 Gram-Schmidt process/159 Notes Calculating projections Problem 5.pdf 1.1 MB
10 Properties of matrix transformations/126 Slides Composition of linear transformations.pdf 1.1 MB
06 Row space, column space, and nullspace of a matrix/079 Slides How to find the nullspace Problem 8.pdf 1.1 MB
15 Diagonalization/191 Slides Why you should love diagonal matrices.pdf 1.0 MB
08 Matrix transformations from R^n to R^m/101 Notes Kernel Problem 4.pdf 1.0 MB
09 Geometry of matrix transformations on R^2 and R^3/115 Notes Plane symmetry in the 3-space Problem 3.pdf 1.0 MB
08 Matrix transformations from R^n to R^m/106 Notes Linear transformations Problem 9.pdf 1.0 MB
15 Diagonalization/209 Notes Powers of matrices Problem 8.pdf 997.5 kB
08 Matrix transformations from R^n to R^m/095 Notes When is a function from Rn to Rm linear Approach 2.pdf 991.1 kB
06 Row space, column space, and nullspace of a matrix/075 Notes Determining a basis for a span consisting of a subset of given vectors Problem 5.pdf 986.7 kB
08 Matrix transformations from R^n to R^m/105 Notes Kernel and geometry Problem 8.pdf 985.2 kB
08 Matrix transformations from R^n to R^m/095 Slides When is a function from Rn to Rm linear Approach 2.pdf 985.1 kB
05 Change of basis/057 Slides Our unifying example and bases.pdf 981.0 kB
04 Coordinates, basis, and dimension/048 Slides Coordinates with respect to a basis.pdf 967.4 kB
03 Linear combinations and linear independence/035 Notes Linear independence in the space of functions Problem 8.pdf 958.5 kB
03 Linear combinations and linear independence/032 Slides An important remark on linear independence in Rn.pdf 956.5 kB
03 Linear combinations and linear independence/038 Slides Wronskian and linear independence for smooth functions.pdf 953.4 kB
08 Matrix transformations from R^n to R^m/104 Notes Linear transformations Problem 7.pdf 953.3 kB
07 Rank, nullity, and four fundamental matrix spaces/083 Slides Nullity.pdf 950.2 kB
06 Row space, column space, and nullspace of a matrix/078 Slides Nullspace for a matrix.pdf 937.7 kB
02 Real vector spaces and their subspaces/009 Slides Cancellation property.pdf 929.9 kB
03 Linear combinations and linear independence/037 Notes Linear independence for smooth functions Problem 9.pdf 916.6 kB
09 Geometry of matrix transformations on R^2 and R^3/116 Notes Projections on planes in the 3-space Problem 4.pdf 913.9 kB
12 Gram-Schmidt process/160 Slides Gram Schmidt Process.pdf 893.5 kB
12 Gram-Schmidt process/148 Slides Orthonormal bases are awesome Reason 3 Transition matrix.pdf 871.7 kB
02 Real vector spaces and their subspaces/018 Notes Subspace Problem 4.pdf 864.7 kB
04 Coordinates, basis, and dimension/041 Slides What is a basis and dimension.pdf 856.6 kB
02 Real vector spaces and their subspaces/015 Slides Subspace Problem 1.pdf 852.4 kB
02 Real vector spaces and their subspaces/010 Slides Two properties of vector spaces Definition of difference.pdf 849.0 kB
07 Rank, nullity, and four fundamental matrix spaces/082 Slides Rank of a matrix.pdf 830.9 kB
03 Linear combinations and linear independence/040 Notes Linear independence for smooth functions Problem 11.pdf 828.9 kB
05 Change of basis/056 Slides Previous example with transition matrix.pdf 822.8 kB
02 Real vector spaces and their subspaces/004 Slides Our prototype.pdf 820.5 kB
12 Gram-Schmidt process/163 Slides Gram Schmidt Process Problem 7.pdf 818.2 kB
02 Real vector spaces and their subspaces/003 Slides From concrete to abstract.pdf 817.2 kB
13 Orthogonal matrices/164 Slides Product of a matrix and its transposed is symmetric.pdf 816.8 kB
12 Gram-Schmidt process/158 Notes Calculating projections Problem 4.pdf 813.4 kB
04 Coordinates, basis, and dimension/052 Notes Bases in a space of functions Problem 7.pdf 798.1 kB
04 Coordinates, basis, and dimension/049 Notes Coordinates with respect to a basis are unique.pdf 796.2 kB
15 Diagonalization/192 Slides Similar matrices.pdf 795.7 kB
02 Real vector spaces and their subspaces/018 Slides Subspace Problem 4.pdf 795.3 kB
03 Linear combinations and linear independence/040 Slides Linear independence for smooth functions Problem 11.pdf 789.6 kB
06 Row space, column space, and nullspace of a matrix/081 Slides Nullspace Problem 10.pdf 771.5 kB
13 Orthogonal matrices/168 Slides Useful formulas for the coming proofs.pdf 767.1 kB
13 Orthogonal matrices/174 Notes Property 6 Product of orthogonal matrices is orthogonal.pdf 750.1 kB
08 Matrix transformations from R^n to R^m/098 Slides Matrix transformations Problem 1.pdf 747.9 kB
06 Row space, column space, and nullspace of a matrix/073 Notes Determining a basis for a span Problem 3.pdf 744.3 kB
06 Row space, column space, and nullspace of a matrix/073 Slides Determining a basis for a span Problem 3.pdf 717.6 kB
05 Change of basis/065 Notes Change of basis Problem 4.pdf 717.3 kB
07 Rank, nullity, and four fundamental matrix spaces/086 Slides Relationship between rank and nullity, Problem 2.pdf 714.9 kB
12 Gram-Schmidt process/151 Slides Coordinates in orthogonal bases Theorem and proof.pdf 712.8 kB
15 Diagonalization/209 Slides Powers of matrices Problem 8.pdf 687.4 kB
10 Properties of matrix transformations/123 Notes Transformations of straight lines Problem 2.pdf 686.2 kB
09 Geometry of matrix transformations on R^2 and R^3/111 Notes Symmetry about a line Problem 2.pdf 684.1 kB
04 Coordinates, basis, and dimension/044 Notes Bases in the 3 space Problem 2.pdf 681.8 kB
02 Real vector spaces and their subspaces/002 Slides From abstract to concrete.pdf 669.3 kB
03 Linear combinations and linear independence/021 Slides Linear combinations New stuff Example 1.pdf 667.8 kB
15 Diagonalization/210 Notes Diagonalization Problem 9.pdf 664.1 kB
13 Orthogonal matrices/173 Slides Property 5 Preserving distances and angles.pdf 663.0 kB
13 Orthogonal matrices/176 Notes Orthogonal matrices Problem 2.pdf 653.3 kB
06 Row space, column space, and nullspace of a matrix/078 Notes Nullspace for a matrix.pdf 651.6 kB
08 Matrix transformations from R^n to R^m/098 Notes Matrix transformations Problem 1.pdf 651.2 kB
06 Row space, column space, and nullspace of a matrix/076 Notes A tricky one Let rows become columns Problem 6.pdf 643.2 kB
07 Rank, nullity, and four fundamental matrix spaces/087 Slides Relationship between rank and nullity, Problem 3.pdf 627.6 kB
09 Geometry of matrix transformations on R^2 and R^3/119 Slides Rotations in the 3-space Problem 7.pdf 626.5 kB
15 Diagonalization/210 Slides Diagonalization Problem 9.pdf 621.0 kB
06 Row space, column space, and nullspace of a matrix/069 Slides Row space and column space for a matrix.pdf 612.2 kB
15 Diagonalization/198 Slides Eigenspaces Geometric and algebraic multiplicity of eigenvalues.pdf 611.4 kB
03 Linear combinations and linear independence/039 Slides Linear independence for smooth functions Problem 10.pdf 607.2 kB
02 Real vector spaces and their subspaces/011 Slides Some properties of vector spaces.pdf 605.4 kB
12 Gram-Schmidt process/154 Notes Orthonormal bases Problem 3.pdf 597.3 kB
03 Linear combinations and linear independence/039 Notes Linear independence for smooth functions Problem 10.pdf 595.9 kB
08 Matrix transformations from R^n to R^m/104 Slides Linear transformations Problem 7.pdf 595.2 kB
08 Matrix transformations from R^n to R^m/106 Slides Linear transformations Problem 9.pdf 593.0 kB
14 Eigenvalues and eigenvectors/181 Slides Eigenvalues and eigenvectors Problem 1.pdf 592.7 kB
11 General linear transformations in different bases/142 Notes Linear transformations Problem 10.pdf 589.7 kB
14 Eigenvalues and eigenvectors/178 Slides Eigenvalues and eigenvectors The terms.pdf 588.1 kB
04 Coordinates, basis, and dimension/049 Slides Coordinates with respect to a basis are unique.pdf 582.8 kB
08 Matrix transformations from R^n to R^m/100 Notes Basis for the image Problem 3.pdf 581.6 kB
04 Coordinates, basis, and dimension/045 Slides Bases in the 4 space Problem 3.pdf 578.5 kB
13 Orthogonal matrices/170 Notes Property 2 Each orthogonal matrix is invertible and the inverse is also orthogonal.pdf 575.6 kB
03 Linear combinations and linear independence/033 Slides Linearly independent generators Problem 6.pdf 571.5 kB
12 Gram-Schmidt process/155 Notes Projection Theorem 1.pdf 558.2 kB
13 Orthogonal matrices/168 Notes Useful formulas for the coming proofs.pdf 554.1 kB
02 Real vector spaces and their subspaces/009 Notes Cancellation property.pdf 550.9 kB
04 Coordinates, basis, and dimension/047 Notes Bases in the space of polynomials Problem 5.pdf 544.3 kB
08 Matrix transformations from R^n to R^m/096 Slides When is a function from Rn to Rm linear Approach 3.pdf 542.0 kB
08 Matrix transformations from R^n to R^m/091 Slides What do we mean by linear.pdf 541.2 kB
12 Gram-Schmidt process/150 Slides Coordinates in ON bases Problem 1.pdf 537.5 kB
06 Row space, column space, and nullspace of a matrix/080 Slides Nullspace Problem 9.pdf 537.0 kB
09 Geometry of matrix transformations on R^2 and R^3/108 Notes An example with nontrivial kernel.pdf 516.8 kB
02 Real vector spaces and their subspaces/005 Notes Formal definition of vector spaces Example 1.pdf 516.0 kB
08 Matrix transformations from R^n to R^m/094 Slides When is a function from Rn to Rm linear Approach 1.pdf 513.0 kB
15 Diagonalization/204 Notes Diagonalizability Problem 4.pdf 507.2 kB
14 Eigenvalues and eigenvectors/184 Slides Finding eigenvalues and eigenvectors Short and sweet.pdf 507.1 kB
06 Row space, column space, and nullspace of a matrix/076 Slides A tricky one Let rows become columns Problem 6.pdf 504.7 kB
12 Gram-Schmidt process/147 Slides Orthonormal bases are awesome Reason 2 Dot product.pdf 491.9 kB
15 Diagonalization/203 Slides Diagonalizability Problem 3.pdf 489.4 kB
05 Change of basis/065 Slides Change of basis Problem 4.pdf 487.3 kB
06 Row space, column space, and nullspace of a matrix/072 Slides Column space Problem 2.pdf 487.0 kB
02 Real vector spaces and their subspaces/014 Slides All the subspace in R3.pdf 483.9 kB
15 Diagonalization/205 Notes Diagonalizability Problem 5.pdf 479.6 kB
04 Coordinates, basis, and dimension/044 Slides Bases in the 3 space Problem 2.pdf 476.4 kB
15 Diagonalization/208 Slides Powers of matrices.pdf 470.0 kB
05 Change of basis/053 Slides Coordinates in different bases.pdf 467.2 kB
07 Rank, nullity, and four fundamental matrix spaces/085 Notes Relationship between rank and nullity, Problem 1.pdf 460.5 kB
15 Diagonalization/206 Notes Diagonalizability Problem 6.pdf 459.5 kB
15 Diagonalization/201 Slides Sufficient but not necessary condition for diagonalizability.pdf 445.3 kB
08 Matrix transformations from R^n to R^m/102 Slides Image and kernel Problem 5.pdf 444.7 kB
08 Matrix transformations from R^n to R^m/101 Slides Kernel Problem 4.pdf 444.4 kB
08 Matrix transformations from R^n to R^m/103 Slides Inverse operators Problem 6.pdf 444.0 kB
10 Properties of matrix transformations/130 Slides Compositions of linear transformations Problem 5.pdf 435.7 kB
14 Eigenvalues and eigenvectors/181 Notes Eigenvalues and eigenvectors Problem 1.pdf 434.4 kB
02 Real vector spaces and their subspaces/016 Slides Subspace Problem 2.pdf 430.5 kB
12 Gram-Schmidt process/157 Slides Projection Formula An illustration in the 3-space.pdf 428.8 kB
12 Gram-Schmidt process/158 Slides Calculating projections Problem 4.pdf 428.6 kB
12 Gram-Schmidt process/156 Slides Projection Theorem 2.pdf 426.7 kB
13 Orthogonal matrices/167 Slides A 3 by 3 example.pdf 426.2 kB
13 Orthogonal matrices/167 Notes A 3 by 3 example.pdf 423.6 kB
09 Geometry of matrix transformations on R^2 and R^3/112 Notes Rotation by 90 degrees about the origin.pdf 410.1 kB
10 Properties of matrix transformations/130 Article-Solved-Problems-Compositions-of-Linear-Transformations.pdf 406.2 kB
13 Orthogonal matrices/170 Slides Property 2 Each orthogonal matrix is invertible and the inverse is also orthogonal.pdf 403.3 kB
12 Gram-Schmidt process/145 Slides Orthonormal bases are awesome.pdf 402.7 kB
04 Coordinates, basis, and dimension/047 Slides Bases in the space of polynomials Problem 5.pdf 396.2 kB
13 Orthogonal matrices/175 Slides Orthogonal matrices Problem 1.pdf 391.2 kB
14 Eigenvalues and eigenvectors/187 Slides Eigenvalues and eigenvectors Problem 4.pdf 382.0 kB
14 Eigenvalues and eigenvectors/186 Slides Eigenvalues and eigenvectors Problem 3.pdf 381.8 kB
01 Introduction to the course/001 List_of_all_Videos_and_Problems_Linear_Algebra_and_Geometry_2.pdf 374.8 kB
08 Matrix transformations from R^n to R^m/093 Slides How to think about functions from Rn to Rm.pdf 374.1 kB
09 Geometry of matrix transformations on R^2 and R^3/109 Notes Line symmetries in the plane.pdf 372.6 kB
13 Orthogonal matrices/171 Slides Property 3 Orthonormal columns and rows.pdf 359.6 kB
08 Matrix transformations from R^n to R^m/100 Slides Basis for the image Problem 3.pdf 358.5 kB
03 Linear combinations and linear independence/023 Slides Linear combinations Problem 1.pdf 352.1 kB
15 Diagonalization/207 Slides Diagonalizability Problem 7.pdf 349.7 kB
10 Properties of matrix transformations/123 Slides Transformations of straight lines Problem 2.pdf 345.8 kB
11 General linear transformations in different bases/138 Slides Linear transformations in different bases.pdf 344.4 kB
02 Real vector spaces and their subspaces/005 Slides Formal definition of vector spaces Example 1.pdf 343.8 kB
12 Gram-Schmidt process/162 Slides Gram Schmidt Process Problem 6.pdf 338.1 kB
12 Gram-Schmidt process/153 Slides Coordinates in orthogonal bases Problem 2.pdf 337.4 kB
10 Properties of matrix transformations/121 Slides What happens with vector subspaces and affine subspaces under linear transformations.pdf 324.8 kB
09 Geometry of matrix transformations on R^2 and R^3/116 Slides Projections on planes in the 3-space Problem 4.pdf 322.9 kB
09 Geometry of matrix transformations on R^2 and R^3/115 Slides Plane symmetry in the 3-space Problem 3.pdf 322.3 kB
16 Wrap-up Linear Algebra and Geometry 2/213 Slides Yes There will be Part 3.pdf 321.8 kB
02 Real vector spaces and their subspaces/017 Slides Subspace Problem 3.pdf 312.9 kB
04 Coordinates, basis, and dimension/051 Slides Dimension of a subspace Problem 6.pdf 308.2 kB
14 Eigenvalues and eigenvectors/188 Slides Eigenvalues and eigenvectors Problem 5.pdf 306.3 kB
14 Eigenvalues and eigenvectors/189 Slides Eigenvalues and eigenvectors Problem 6.pdf 306.2 kB
08 Matrix transformations from R^n to R^m/092 Slides Some terminology.pdf 304.8 kB
06 Row space, column space, and nullspace of a matrix/077 Slides A basis in the space of polynomials Problem 7.pdf 304.3 kB
06 Row space, column space, and nullspace of a matrix/075 Slides Determining a basis for a span consisting of a subset of given vectors Problem 5.pdf 304.0 kB
06 Row space, column space, and nullspace of a matrix/074 Slides Determining a basis for a span consisting of a subset of given vectors Problem 4.pdf 302.5 kB
05 Change of basis/062 Slides Change of basis Problem 1.pdf 300.4 kB
11 General linear transformations in different bases/140 Slides Linear transformations in different bases Problem 8.pdf 300.3 kB
11 General linear transformations in different bases/139 Slides Linear transformations in different bases Problem 7.pdf 299.7 kB
02 Real vector spaces and their subspaces/012 Slides What is a subspace.pdf 294.8 kB
12 Gram-Schmidt process/159 Slides Calculating projections Problem 5.pdf 285.2 kB
04 Coordinates, basis, and dimension/042 Slides Bases in the 3 space Problem 1.pdf 276.6 kB
11 General linear transformations in different bases/135 Slides Linear transformations Problem 4.pdf 276.0 kB
11 General linear transformations in different bases/137 Slides Linear transformations Problem 6.pdf 270.7 kB
12 Gram-Schmidt process/152 Slides Each orthogonal set is linearly independent Proof.pdf 269.8 kB
03 Linear combinations and linear independence/037 Slides Linear independence for smooth functions Problem 9.pdf 267.4 kB
09 Geometry of matrix transformations on R^2 and R^3/108 Slides An example with nontrivial kernel.pdf 265.9 kB
12 Gram-Schmidt process/146 Slides Orthonormal bases are awesome Reason 1 Distance.pdf 265.0 kB
11 General linear transformations in different bases/133 Slides Linear transformations Problem 2.pdf 261.3 kB
03 Linear combinations and linear independence/034 Slides Linear independence in the set of matrices Problem 7.pdf 251.4 kB
10 Properties of matrix transformations/129 Slides Compositions of linear transformations Problem 4.pdf 243.9 kB
15 Diagonalization/200 Slides Eigenvectors corresponding to different eigenvalues are linearly independent.pdf 242.6 kB
07 Rank, nullity, and four fundamental matrix spaces/085 Slides Relationship between rank and nullity, Problem 1.pdf 241.4 kB
12 Gram-Schmidt process/149 Slides Orthonormal bases are awesome Reason 4 Coordinates.pdf 241.1 kB
11 General linear transformations in different bases/141 Slides Linear transformations in different bases Problem 9.pdf 239.4 kB
15 Diagonalization/199 Slides Eigenspaces Problem 2.pdf 236.9 kB
11 General linear transformations in different bases/143 Slides Linear transformations Problem 11.pdf 236.6 kB
11 General linear transformations in different bases/142 Slides Linear transformations Problem 10.pdf 236.6 kB
04 Coordinates, basis, and dimension/052 Slides Bases in a space of functions Problem 7.pdf 234.4 kB
13 Orthogonal matrices/176 Slides Orthogonal matrices Problem 2.pdf 229.3 kB
03 Linear combinations and linear independence/026 Slides Span Problem 3.pdf 221.1 kB
05 Change of basis/066 Slides Change of basis Problem 5.pdf 218.7 kB
12 Gram-Schmidt process/154 Slides Orthonormal bases Problem 3.pdf 213.3 kB
03 Linear combinations and linear independence/028 Slides Span Problem 5.pdf 212.0 kB
11 General linear transformations in different bases/134 Slides Linear transformations Problem 3.pdf 211.6 kB
11 General linear transformations in different bases/136 Slides Linear transformations Problem 5.pdf 210.9 kB
05 Change of basis/064 Slides Change of basis Problem 3.pdf 206.2 kB
11 General linear transformations in different bases/132 Slides Linear transformations Problem 1.pdf 203.0 kB
03 Linear combinations and linear independence/027 Slides Span Problem 4.pdf 201.9 kB
02 Real vector spaces and their subspaces/008 Slides Vector spaces Example 4 Complex numbers.pdf 196.1 kB
04 Coordinates, basis, and dimension/046 Slides Bases in the 4 space Problem 4.pdf 187.4 kB
03 Linear combinations and linear independence/024 Slides Linear combinations Problem 2.pdf 183.8 kB
08 Matrix transformations from R^n to R^m/105 Slides Kernel and geometry Problem 8.pdf 182.3 kB
06 Row space, column space, and nullspace of a matrix/068 Slides What you are going to learn in this section.pdf 181.6 kB
05 Change of basis/063 Slides Change of basis Problem 2.pdf 174.0 kB
03 Linear combinations and linear independence/022 Slides Linear combinations Example 2.pdf 170.8 kB
03 Linear combinations and linear independence/035 Slides Linear independence in the space of functions Problem 8.pdf 164.7 kB
13 Orthogonal matrices/174 Slides Property 6 Product of orthogonal matrices is orthogonal.pdf 163.1 kB
03 Linear combinations and linear independence/029 Slides What do we mean by trivial.pdf 145.6 kB
12 Gram-Schmidt process/163 Article-Solved-Problems-Gram-Schmidt.pdf 143.4 kB
15 Diagonalization/211 Article-Solved-Problems-Diagonalization.pdf 138.3 kB
14 Eigenvalues and eigenvectors/190 Article-Solved-Problems-Eigenvalues.pdf 132.4 kB
10 Properties of matrix transformations/120 Slides What kind of properties we will discuss.pdf 85.9 kB
14 Eigenvalues and eigenvectors/179 Slides Order of defining Order of computing.pdf 66.3 kB
04 Coordinates, basis, and dimension/002 Bases in the 3-space, Problem 1.en.srt 42.4 kB
05 Change of basis/010 Change of basis, Problem 1.en.srt 40.4 kB
11 General linear transformations in different bases/005 Linear transformations, Problem 4.en.srt 40.0 kB
14 Eigenvalues and eigenvectors/009 Eigenvalues and eigenvectors for examples from Video 180.en.srt 33.8 kB
11 General linear transformations in different bases/004 Linear transformations, Problem 3.en.srt 31.4 kB
11 General linear transformations in different bases/002 Linear transformations, Problem 1.en.srt 30.8 kB
08 Matrix transformations from R^n to R^m/009 Image, kernel, and inverse operators, Problem 2.en.srt 30.8 kB
14 Eigenvalues and eigenvectors/013 Eigenvalues and eigenvectors, Problem 6.en.srt 30.0 kB
15 Diagonalization/009 Eigenspaces, Problem 2.en.srt 29.6 kB
14 Eigenvalues and eigenvectors/010 Eigenvalues and eigenvectors, Problem 3.en.srt 29.4 kB
04 Coordinates, basis, and dimension/006 Bases in the 4-space, Problem 4.en.srt 28.0 kB
03 Linear combinations and linear independence/006 Linear combinations, Problem 2.en.srt 27.5 kB
11 General linear transformations in different bases/003 Linear transformations, Problem 2.en.srt 27.5 kB
13 Orthogonal matrices/010 Property 5_ Preserving distances and angles.en.srt 27.2 kB
12 Gram-Schmidt process/007 Coordinates in ON bases, Problem 1.en.srt 26.9 kB
02 Real vector spaces and their subspaces/015 Subspaces, Problem 2.en.srt 26.1 kB
06 Row space, column space, and nullspace of a matrix/014 Nullspace, Problem 10.en.srt 25.0 kB
11 General linear transformations in different bases/009 Linear transformations in different bases, Problem 7.en.srt 24.5 kB
09 Geometry of matrix transformations on R^2 and R^3/013 Rotations in the 3-space, Problem 7.en.srt 24.4 kB
05 Change of basis/012 Change of basis, Problem 3.en.srt 24.4 kB
03 Linear combinations and linear independence/015 Linearly independent generators, Problem 6.en.srt 23.8 kB
09 Geometry of matrix transformations on R^2 and R^3/004 Projection on a given vector, Problem 1.en.srt 22.8 kB
09 Geometry of matrix transformations on R^2 and R^3/012 Projection on a given plane, Problem 6.en.srt 22.6 kB
14 Eigenvalues and eigenvectors/001 Crash course in factoring polynomials.en.srt 22.4 kB
08 Matrix transformations from R^n to R^m/005 When is a function from Rn to Rm linear_ Approach 2.en.srt 22.4 kB
15 Diagonalization/010 Eigenvectors corresponding to different eigenvalues are linearly independent.en.srt 21.8 kB
02 Real vector spaces and their subspaces/016 Subspaces, Problem 3.en.srt 21.5 kB
12 Gram-Schmidt process/013 Projection Theorem 2.en.srt 21.1 kB
14 Eigenvalues and eigenvectors/012 Eigenvalues and eigenvectors, Problem 5.en.srt 21.0 kB
06 Row space, column space, and nullspace of a matrix/003 What are the elementary row operations doing to the row spaces_.en.srt 20.9 kB
10 Properties of matrix transformations/005 Change of area (volume) under linear operators in the plane (space).en.srt 20.9 kB
10 Properties of matrix transformations/011 Compositions of linear transformations, Problem 5.en.srt 20.8 kB
03 Linear combinations and linear independence/018 Vandermonde determinant and polynomials.en.srt 20.4 kB
02 Real vector spaces and their subspaces/011 What is a subspace.en.srt 20.0 kB
02 Real vector spaces and their subspaces/012 All the subspaces in R2.en.srt 19.8 kB
12 Gram-Schmidt process/020 Gram-Schmidt Process, Problem 7.en.srt 19.7 kB
03 Linear combinations and linear independence/019 Linear independence in C^∞(R), Problem 9.en.srt 19.6 kB
12 Gram-Schmidt process/010 Coordinates in orthogonal bases, Problem 2.en.srt 19.5 kB
09 Geometry of matrix transformations on R^2 and R^3/011 Symmetry about a given plane, Problem 5.en.srt 19.5 kB
02 Real vector spaces and their subspaces/004 Formal definition of vector spaces Example 1_ Rn.en.srt 19.2 kB
11 General linear transformations in different bases/006 Linear transformations, Problem 5.en.srt 19.2 kB
14 Eigenvalues and eigenvectors/007 How to compute eigenvectors.en.srt 19.1 kB
06 Row space, column space, and nullspace of a matrix/008 Determining a basis for a span consisting of a subset of given vectors, Prob.en.srt 19.1 kB
14 Eigenvalues and eigenvectors/006 How to compute eigenvalues Characteristic polynomial.en.srt 19.0 kB
11 General linear transformations in different bases/007 Linear transformations in different bases, Problem 6.en.srt 18.8 kB
06 Row space, column space, and nullspace of a matrix/010 A basis in the space of polynomials, Problem 7.en.srt 18.4 kB
02 Real vector spaces and their subspaces/005 Vector spaces, Example 2_ m × n matrices with real entries.en.srt 18.3 kB
06 Row space, column space, and nullspace of a matrix/013 Nullspace, Problem 9.en.srt 18.2 kB
07 Rank, nullity, and four fundamental matrix spaces/003 Relationship between rank and nullity.en.srt 18.2 kB
09 Geometry of matrix transformations on R^2 and R^3/003 Line symmetries in the plane.en.srt 18.0 kB
14 Eigenvalues and eigenvectors/004 Eigenvalues and eigenvectors geometrically.en.srt 18.0 kB
08 Matrix transformations from R^n to R^m/013 Inverse operators, Problem 6.en.srt 18.0 kB
04 Coordinates, basis, and dimension/005 Bases in the 4-space, Problem 3.en.srt 17.8 kB
06 Row space, column space, and nullspace of a matrix/007 Determining a basis for a span consisting of a subset of given vectors, Prob.en.srt 17.5 kB
02 Real vector spaces and their subspaces/006 Vector spaces, Example 3_ real-valued functions on some interval.en.srt 17.2 kB
15 Diagonalization/013 Diagonalizability, Problem 3.en.srt 17.0 kB
09 Geometry of matrix transformations on R^2 and R^3/005 Symmetry about the line y = kx, Problem 2.en.srt 16.9 kB
03 Linear combinations and linear independence/013 Geometry of linear independence and linear dependence.en.srt 16.8 kB
07 Rank, nullity, and four fundamental matrix spaces/009 The Fundamental Theorem of Linear Algebra and Gilbert Strang.en.srt 16.8 kB
10 Properties of matrix transformations/010 Compositions of linear transformations, Problem 4.en.srt 16.6 kB
03 Linear combinations and linear independence/016 Linear independence in the set of matrices, Problem 7.en.srt 16.3 kB
03 Linear combinations and linear independence/009 Span, Problem 4.en.srt 16.3 kB
05 Change of basis/015 Change to an orthonormal basis in R^2.en.srt 16.1 kB
01 Introduction to the course/001 Introduction to the course.en.srt 16.0 kB
03 Linear combinations and linear independence/008 Span, Problem 3.en.srt 16.0 kB
09 Geometry of matrix transformations on R^2 and R^3/001 Our unifying example_ linear transformations and change of basis.en.srt 15.9 kB
10 Properties of matrix transformations/009 Why does it work_.en.srt 15.9 kB
15 Diagonalization/003 Similarity of matrices is an equivalence relation (RST).en.srt 15.6 kB
03 Linear combinations and linear independence/005 Linear combinations, Problem 1.en.srt 15.6 kB
07 Rank, nullity, and four fundamental matrix spaces/007 Orthogonal complements, Problem 4.en.srt 15.5 kB
02 Real vector spaces and their subspaces/010 Some properties of vector spaces.en.srt 15.5 kB
03 Linear combinations and linear independence/012 Linear independence and linear dependence.en.srt 15.3 kB
11 General linear transformations in different bases/010 Linear transformations in different bases, Problem 8.en.srt 15.2 kB
10 Properties of matrix transformations/007 Compositions of linear transformations.en.srt 15.1 kB
04 Coordinates, basis, and dimension/003 Bases in the plane and in the 3-space.en.srt 15.1 kB
15 Diagonalization/008 Eigenspaces; geometric and algebraic multiplicity of eigenvalues.en.srt 14.9 kB
05 Change of basis/008 Two non-standard bases, Method 2.en.srt 14.9 kB
06 Row space, column space, and nullspace of a matrix/006 Determining a basis for a span, Problem 3.en.srt 14.7 kB
05 Change of basis/009 How to recalculate coordinates between two non-standard bases_ An algorithm.en.srt 14.7 kB
05 Change of basis/003 Transition matrix, a derivation.en.srt 14.7 kB
12 Gram-Schmidt process/015 Calculating projections, Problem 4.en.srt 14.6 kB
08 Matrix transformations from R^n to R^m/006 When is a function from Rn to Rm linear_ Approach 3.en.srt 14.2 kB
05 Change of basis/011 Change of basis, Problem 2.en.srt 14.2 kB
08 Matrix transformations from R^n to R^m/002 Some terminology.en.srt 14.2 kB
08 Matrix transformations from R^n to R^m/003 How to think about functions from Rn to Rm_.en.srt 14.0 kB
06 Row space, column space, and nullspace of a matrix/004 What are the elementary row operations doing to the column spaces_.en.srt 13.9 kB
02 Real vector spaces and their subspaces/007 Vector spaces, Example 4_ complex numbers.en.srt 13.9 kB
11 General linear transformations in different bases/011 Linear transformations in different bases, Problem 9.en.srt 13.9 kB
11 General linear transformations in different bases/013 Linear transformations, Problem 11.en.srt 13.8 kB
10 Properties of matrix transformations/004 Transformations of straight lines, Problem 2.en.srt 13.6 kB
06 Row space, column space, and nullspace of a matrix/011 Nullspace for a matrix.en.srt 13.5 kB
15 Diagonalization/006 How to diagonalize a matrix, a recipe.en.srt 13.5 kB
14 Eigenvalues and eigenvectors/011 Eigenvalues and eigenvectors, Problem 4.en.srt 13.5 kB
10 Properties of matrix transformations/006 Change of area under linear transformations, Problem 3.en.srt 13.4 kB
04 Coordinates, basis, and dimension/008 Coordinates with respect to a basis.en.srt 13.4 kB
12 Gram-Schmidt process/012 Projection Theorem 1.en.srt 13.2 kB
02 Real vector spaces and their subspaces/003 Our prototype.en.srt 13.2 kB
12 Gram-Schmidt process/001 Dot product and orthogonality until now.en.srt 13.1 kB
06 Row space, column space, and nullspace of a matrix/005 Column space, Problem 2.en.srt 13.1 kB
13 Orthogonal matrices/012 Orthogonal matrices, Problem 1.en.srt 12.9 kB
08 Matrix transformations from R^n to R^m/007 Approaches 2 and 3 are equivalent.en.srt 12.8 kB
09 Geometry of matrix transformations on R^2 and R^3/009 Plane symmetry in the 3-space, Problem 3.en.srt 12.7 kB
09 Geometry of matrix transformations on R^2 and R^3/008 Expansion, compression, scaling, and shear.en.srt 12.6 kB
02 Real vector spaces and their subspaces/009 Two properties of vector spaces; Definition of difference.en.srt 12.5 kB
12 Gram-Schmidt process/019 Gram-Schmidt Process, Problem 6.en.srt 12.5 kB
15 Diagonalization/017 Diagonalizability, Problem 7.en.srt 12.5 kB
10 Properties of matrix transformations/003 Parallel lines transform into parallel lines, Problem 1.en.srt 12.1 kB
06 Row space, column space, and nullspace of a matrix/009 A tricky one_ Let rows become columns, Problem 6.en.srt 12.0 kB
03 Linear combinations and linear independence/002 Linear combinations in Part 1.en.srt 11.7 kB
08 Matrix transformations from R^n to R^m/016 Linear transformations, Problem 9.en.srt 11.7 kB
10 Properties of matrix transformations/008 How to obtain the standard matrix of a composition of linear transformations.en.srt 11.7 kB
05 Change of basis/014 Change of basis, Problem 5.en.srt 11.6 kB
09 Geometry of matrix transformations on R^2 and R^3/006 Rotation by 90 degrees about the origin.en.srt 11.5 kB
08 Matrix transformations from R^n to R^m/012 Image and kernel, Problem 5.en.srt 11.5 kB
15 Diagonalization/012 Necessary and sufficient condition for diagonalizability.en.srt 11.4 kB
06 Row space, column space, and nullspace of a matrix/002 Row space and column space for a matrix.en.srt 11.4 kB
09 Geometry of matrix transformations on R^2 and R^3/002 An example with nontrivial kernel.en.srt 11.2 kB
02 Real vector spaces and their subspaces/013 All the subspaces in R3.en.srt 11.2 kB
09 Geometry of matrix transformations on R^2 and R^3/007 Rotation by the angle α about the origin.en.srt 11.1 kB
04 Coordinates, basis, and dimension/012 Bases in a space of functions, Problem 7.en.srt 11.0 kB
12 Gram-Schmidt process/017 Gram-Schmidt Process.en.srt 11.0 kB
04 Coordinates, basis, and dimension/011 Dimension of a subspace, Problem 6.en.srt 10.9 kB
02 Real vector spaces and their subspaces/017 Subspaces, Problem 4.en.srt 10.9 kB
05 Change of basis/005 Our unifying example.en.srt 10.7 kB
08 Matrix transformations from R^n to R^m/011 Kernel, Problem 4.en.srt 10.6 kB
03 Linear combinations and linear independence/014 An important remark on linear independence in Rn.en.srt 10.6 kB
03 Linear combinations and linear independence/017 Linear independence in C^0[−∞, ∞], Problem 8.en.srt 10.6 kB
03 Linear combinations and linear independence/020 Wronskian and linear independence in C∞(R).en.srt 10.6 kB
08 Matrix transformations from R^n to R^m/014 Linear transformations, Problem 7.en.srt 10.6 kB
07 Rank, nullity, and four fundamental matrix spaces/004 Relationship between rank and nullity, Problem 1.en.srt 10.3 kB
02 Real vector spaces and their subspaces/014 Subspaces, Problem 1.en.srt 10.1 kB
08 Matrix transformations from R^n to R^m/004 When is a function from Rn to Rm linear_ Approach 1.en.srt 9.9 kB
15 Diagonalization/020 Diagonalization, Problem 9.en.srt 9.8 kB
08 Matrix transformations from R^n to R^m/015 Kernel and geometry, Problem 8.en.srt 9.8 kB
15 Diagonalization/001 Why you should love diagonal matrices.en.srt 9.7 kB
03 Linear combinations and linear independence/007 What is a span, definition and some examples.en.srt 9.4 kB
03 Linear combinations and linear independence/022 Linear independence in C^∞(R), Problem 11.en.srt 9.3 kB
07 Rank, nullity, and four fundamental matrix spaces/005 Relationship between rank and nullity, Problem 2.en.srt 9.2 kB
14 Eigenvalues and eigenvectors/014 Eigenvalues and eigenvectors, Problem 7.en.srt 9.2 kB
04 Coordinates, basis, and dimension/001 What is a basis and dimension_.en.srt 9.1 kB
06 Row space, column space, and nullspace of a matrix/012 How to find the nullspace, Problem 8.en.srt 9.0 kB
12 Gram-Schmidt process/008 Coordinates in orthogonal bases, Theorem and proof.en.srt 9.0 kB
10 Properties of matrix transformations/002 What happens with vector subspaces and affine subspaces under linear transfo.en.srt 8.9 kB
13 Orthogonal matrices/009 Property 4_ Orthogonal matrices are transition matrices between ON-bases.en.srt 8.9 kB
05 Change of basis/007 Two non-standard bases, Method 1.en.srt 8.8 kB
15 Diagonalization/019 Powers of matrices, Problem 8.en.srt 8.8 kB
05 Change of basis/013 Change of basis, Problem 4.en.srt 8.8 kB
13 Orthogonal matrices/013 Orthogonal matrices, Problem 2.en.srt 8.8 kB
11 General linear transformations in different bases/008 Linear transformations in different bases.en.srt 8.5 kB
04 Coordinates, basis, and dimension/009 Coordinates with respect to a basis are unique.en.srt 8.4 kB
13 Orthogonal matrices/006 Property 1_ Determinant of each orthogonal matrix is 1 or −1.en.srt 8.3 kB
13 Orthogonal matrices/002 Definition and examples of orthogonal matrices.en.srt 8.3 kB
12 Gram-Schmidt process/016 Calculating projections, Problem 5.en.srt 8.2 kB
08 Matrix transformations from R^n to R^m/010 Basis for the image, Problem 3.en.srt 8.2 kB
15 Diagonalization/015 Diagonalizability, Problem 5.en.srt 8.1 kB
15 Diagonalization/004 Shared properties of similar matrices.en.srt 8.1 kB
13 Orthogonal matrices/003 Geometry of 2-by-2 orthogonal matrices.en.srt 8.1 kB
16 Wrap-up Linear Algebra and Geometry 2/001 Linear Algebra and Geometry 2, Wrap-up.en.srt 8.0 kB
12 Gram-Schmidt process/002 Orthonormal bases are awesome.en.srt 7.9 kB
13 Orthogonal matrices/005 Useful formulas for the coming proofs.en.srt 7.9 kB
09 Geometry of matrix transformations on R^2 and R^3/010 Projections on planes in the 3-space, Problem 4.en.srt 7.8 kB
08 Matrix transformations from R^n to R^m/001 What do we mean by linear_.en.srt 7.8 kB
15 Diagonalization/007 Diagonalize our favourite matrix.en.srt 7.7 kB
05 Change of basis/002 It is easy to recalculate from the standard basis.en.srt 7.7 kB
12 Gram-Schmidt process/014 Projection Formula, an illustration in the 3-space.en.srt 7.6 kB
12 Gram-Schmidt process/018 Gram-Schmidt Process, Our unifying example.en.srt 7.6 kB
13 Orthogonal matrices/004 A 3-by-3 example.en.srt 7.5 kB
03 Linear combinations and linear independence/001 Our unifying example.en.srt 7.4 kB
11 General linear transformations in different bases/012 Linear transformations, Problem 10.en.srt 7.4 kB
08 Matrix transformations from R^n to R^m/008 Matrix transformations, Problem 1.en.srt 7.3 kB
05 Change of basis/001 Coordinates in different bases.en.srt 7.2 kB
03 Linear combinations and linear independence/011 What do we mean by trivial_.en.srt 7.0 kB
03 Linear combinations and linear independence/003 Linear combinations, new stuff. Example 1.en.srt 6.9 kB
12 Gram-Schmidt process/011 Orthonormal bases, Problem 3.en.srt 6.9 kB
12 Gram-Schmidt process/009 Each orthogonal set is linearly independent, Proof.en.srt 6.9 kB
11 General linear transformations in different bases/001 Linear transformations between two linear spaces.en.srt 6.9 kB
07 Rank, nullity, and four fundamental matrix spaces/008 Four fundamental matrix spaces.en.srt 6.7 kB
06 Row space, column space, and nullspace of a matrix/001 What you are going to learn in this section.en.srt 6.5 kB
02 Real vector spaces and their subspaces/008 Cancellation property.en.srt 6.5 kB
13 Orthogonal matrices/001 Product of a matrix and its transposed is symmetric.en.srt 6.3 kB
13 Orthogonal matrices/011 Property 6_ Product of orthogonal matrices is orthogonal.en.srt 6.2 kB
14 Eigenvalues and eigenvectors/008 Finding eigenvalues and eigenvectors_ short and sweet.en.srt 6.1 kB
15 Diagonalization/021 Sneak peek into the next course; orthogonal diagonalization.en.srt 6.1 kB
07 Rank, nullity, and four fundamental matrix spaces/001 Rank of a matrix.en.srt 6.1 kB
03 Linear combinations and linear independence/021 Linear independence in C^∞(R), Problem 10.en.srt 6.1 kB
05 Change of basis/006 One more simple example and bases.en.srt 5.8 kB
03 Linear combinations and linear independence/004 Linear combinations Example 2.en.srt 5.8 kB
10 Properties of matrix transformations/001 What kind of properties we will discuss.en.srt 5.8 kB
13 Orthogonal matrices/008 Property 3_ Orthonormal columns and rows.en.srt 5.7 kB
05 Change of basis/004 Previous example with transition matrix.en.srt 5.6 kB
15 Diagonalization/018 Powers of matrices.en.srt 5.5 kB
14 Eigenvalues and eigenvectors/005 Eigenvalues and eigenvectors, Problem 1.en.srt 5.4 kB
04 Coordinates, basis, and dimension/004 Bases in the 3-space, Problem 2.en.srt 5.4 kB
13 Orthogonal matrices/007 Property 2_ Each orthogonal matrix A is invertible and A−1 is also orthogona.en.srt 5.3 kB
15 Diagonalization/016 Diagonalizability, Problem 6.en.srt 5.3 kB
12 Gram-Schmidt process/006 Orthonormal bases are awesome, Reason 4_ coordinates.en.srt 5.2 kB
04 Coordinates, basis, and dimension/010 Coordinates in our unifying example.en.srt 5.1 kB
15 Diagonalization/014 Diagonalizability, Problem 4.en.srt 5.0 kB
15 Diagonalization/005 Diagonalizable matrices.en.srt 4.8 kB
04 Coordinates, basis, and dimension/007 Bases in the space of polynomials, Problem 5.en.srt 4.7 kB
12 Gram-Schmidt process/004 Orthonormal bases are awesome, Reason 2_ dot product.en.srt 4.5 kB
02 Real vector spaces and their subspaces/001 From abstract to concrete.en.srt 4.1 kB
16 Wrap-up Linear Algebra and Geometry 2/002 Yes, there will be Part 3!.en.srt 4.0 kB
02 Real vector spaces and their subspaces/002 From concrete to abstract.en.srt 4.0 kB
12 Gram-Schmidt process/005 Orthonormal bases are awesome, Reason 3_ transition matrix.en.srt 3.8 kB
07 Rank, nullity, and four fundamental matrix spaces/006 Relationship between rank and nullity, Problem 3.en.srt 3.5 kB
15 Diagonalization/002 Similar matrices.en.srt 3.2 kB
15 Diagonalization/011 A sufficient, but not necessary, condition for diagonalizability.en.srt 3.1 kB
12 Gram-Schmidt process/003 Orthonormal bases are awesome, Reason 1_ distance.en.srt 2.9 kB
07 Rank, nullity, and four fundamental matrix spaces/002 Nullity.en.srt 2.7 kB
14 Eigenvalues and eigenvectors/002 Eigenvalues and eigenvectors, the terms.en.srt 2.7 kB
03 Linear combinations and linear independence/010 Span, Problem 5.en.srt 2.5 kB
14 Eigenvalues and eigenvectors/003 Order of defining, order of computing.en.srt 2.1 kB
16 Wrap-up Linear Algebra and Geometry 2/003 Final words.en.srt 668 Bytes

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