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3. More problem solving; spaces different from R^n/5. In the space of polynomials, Problem 5.mp4 1.0 GB
3. More problem solving; spaces different from R^n/1. Eigendecomposition, Problem 1.mp4 935.0 MB
3. More problem solving; spaces different from R^n/4. Powers and roots, Problem 4.mp4 805.7 MB
3. More problem solving; spaces different from R^n/2. Eigendecomposition, Problem 2.mp4 607.7 MB
2. Geometrical operators in the plane and in the 3-space/12. Spectral decomposition, Geometrical illustration, Problem 8.mp4 597.8 MB
7. Inner product as a generalization of dot product/14. Gram matrix, Problem 3.mp4 591.8 MB
2. Geometrical operators in the plane and in the 3-space/7. Problem 5 Projection in the 3-space.mp4 588.5 MB
9. Projections and Gram–Schmidt process in various inner product spaces/4. Orthonormal sets of continuous functions, Problem 1.mp4 585.8 MB
14. The Grand Finale Singular Value Decomposition and Pseudoinverses/9. More new facts about AT A six equivalent statements.mp4 562.6 MB
3. More problem solving; spaces different from R^n/7. In the space of matrices, Problem 7.mp4 532.3 MB
2. Geometrical operators in the plane and in the 3-space/6. Problem 4 Projection in the 3-space.mp4 523.8 MB
5. Recurrence relations, dynamical systems, Markov matrices/12. Steady-state vector (equilibrium vector), Problem 7.mp4 523.3 MB
3. More problem solving; spaces different from R^n/3. Powers and roots, Problem 3.mp4 512.9 MB
8. Norm, distance, angles, and orthogonality in inner product spaces/9. Cauchy-Schwarz inequality, proof 1.mp4 469.8 MB
12. Quadratic forms and their classification/17. Quadratic surfaces, shortest distance, Problem 8.mp4 457.4 MB
11. Diagonalization of symmetric matrices/17. Pos and neg definite matrices, semidefinite and indefinite matrices, Problem 9.mp4 455.3 MB
11. Diagonalization of symmetric matrices/5. Eigenvalues for a (real) symmetric matrix are real.mp4 448.6 MB
14. The Grand Finale Singular Value Decomposition and Pseudoinverses/7. SVD, reduced singular value decomposition, Problem 1.mp4 444.1 MB
14. The Grand Finale Singular Value Decomposition and Pseudoinverses/6. Singular value decomposition with proof and geometric interpretation.mp4 442.6 MB
12. Quadratic forms and their classification/1. The correspondence between quadratic forms and symmetric matrices is 1-to-1.mp4 435.1 MB
4. Intermezzo isomorphic vector spaces/12. Vector spaces, fields, rings, Problem 5.mp4 433.1 MB
5. Recurrence relations, dynamical systems, Markov matrices/4. Systems of difference equations, Problem 1.mp4 432.4 MB
4. Intermezzo isomorphic vector spaces/4. A necessary condition for isomorphic vector spaces.mp4 425.4 MB
8. Norm, distance, angles, and orthogonality in inner product spaces/10. Cauchy-Schwarz inequality, proof 2.mp4 419.4 MB
9. Projections and Gram–Schmidt process in various inner product spaces/13. Gram-Schmidt in IP spaces, Problem 7.mp4 417.2 MB
4. Intermezzo isomorphic vector spaces/11. Vector spaces, fields, rings, Problem 4.mp4 416.8 MB
6. Solving systems of linear ODE, and solving higher order ODE/10. Another way of looking at the same problem.mp4 412.4 MB
9. Projections and Gram–Schmidt process in various inner product spaces/9. Orthogonal projections on subspaces of an IP space, Problem 4.mp4 391.8 MB
11. Diagonalization of symmetric matrices/1. The link between symmetric matrices and quadratic forms, Problem 1.mp4 389.8 MB
5. Recurrence relations, dynamical systems, Markov matrices/5. Systems of difference equations, Problem 2.mp4 382.9 MB
7. Inner product as a generalization of dot product/13. Matrix inner products on R^n, Problem 2.mp4 381.6 MB
14. The Grand Finale Singular Value Decomposition and Pseudoinverses/5. ON-bases containing only eigenvectors of certain matrix products.mp4 374.8 MB
12. Quadratic forms and their classification/13. Different roles of symmetric matrices (back to Videos 150 and 168), Problem.mp4 372.4 MB
5. Recurrence relations, dynamical systems, Markov matrices/9. Higher order difference equations, Problem 6.mp4 367.4 MB
7. Inner product as a generalization of dot product/12. Quadratic forms and how to read them.mp4 364.7 MB
2. Geometrical operators in the plane and in the 3-space/5. Problem 3 Symmetry in the 3-space.mp4 364.3 MB
4. Intermezzo isomorphic vector spaces/9. Isomorphic spaces Problem 3.mp4 362.6 MB
10. Min-max problems, best approximations, and least squares/5. Min-max, Problem 4.mp4 361.4 MB
5. Recurrence relations, dynamical systems, Markov matrices/7. Higher order difference equations, Problem 4.mp4 357.8 MB
10. Min-max problems, best approximations, and least squares/6. Min-max, Problem 5.mp4 357.7 MB
8. Norm, distance, angles, and orthogonality in inner product spaces/19. Triangle inequality in inner product spaces.mp4 357.6 MB
10. Min-max problems, best approximations, and least squares/2. Min-max, Problem 1.mp4 354.2 MB
11. Diagonalization of symmetric matrices/12. Orthogonal diagonalization, Problem 4.mp4 351.3 MB
14. The Grand Finale Singular Value Decomposition and Pseudoinverses/11. Pseudoinverse, Problem 3.mp4 349.2 MB
12. Quadratic forms and their classification/11. Classification of curves, Problem 4.mp4 344.1 MB
8. Norm, distance, angles, and orthogonality in inner product spaces/23. Generalized Theorem of Pythagoras, Problem 10.mp4 331.1 MB
3. More problem solving; spaces different from R^n/6. In the space of polynomials, Problem 6.mp4 326.8 MB
5. Recurrence relations, dynamical systems, Markov matrices/15. Markov matrices, Problem 10, Election.mp4 312.3 MB
5. Recurrence relations, dynamical systems, Markov matrices/8. Higher order difference equations, Problem 5.mp4 311.0 MB
6. Solving systems of linear ODE, and solving higher order ODE/5. The method.mp4 307.0 MB
11. Diagonalization of symmetric matrices/14. Orthogonal diagonalization, Problem 6.mp4 301.8 MB
10. Min-max problems, best approximations, and least squares/19. Least squares straight line fit, Problem 12.mp4 299.8 MB
10. Min-max problems, best approximations, and least squares/17. Least squares, Problem 11, by normal equation.mp4 292.2 MB
12. Quadratic forms and their classification/19. Quadratic surfaces, Problem 10.mp4 290.6 MB
9. Projections and Gram–Schmidt process in various inner product spaces/10. Orthogonal projections on subspaces of an IP space, Problem 5.mp4 288.3 MB
10. Min-max problems, best approximations, and least squares/18. Least squares, Problem 11, by projection.mp4 275.1 MB
5. Recurrence relations, dynamical systems, Markov matrices/13. Markov matrices, Problem 8, Restaurant.mp4 265.2 MB
7. Inner product as a generalization of dot product/9. Weighted Euclidean inner product, Problem 1.mp4 264.7 MB
7. Inner product as a generalization of dot product/5. Inner product spaces.mp4 263.7 MB
7. Inner product as a generalization of dot product/19. The evaluation inner products on P2, Problem 5.mp4 251.9 MB
6. Solving systems of linear ODE, and solving higher order ODE/8. System of ODE, Problem 3.mp4 247.5 MB
9. Projections and Gram–Schmidt process in various inner product spaces/5. Orthogonal complements, Problem 2.mp4 240.2 MB
12. Quadratic forms and their classification/14. Classification of curves, Problem 7.mp4 236.7 MB
12. Quadratic forms and their classification/12. Classification of curves, Problem 5.mp4 235.9 MB
9. Projections and Gram–Schmidt process in various inner product spaces/14. Easy computations of IP in ON bases, Problem 8.mp4 229.3 MB
12. Quadratic forms and their classification/18. Quadratic surfaces, Problem 9.mp4 225.2 MB
5. Recurrence relations, dynamical systems, Markov matrices/16. Dynamical systems, Problem 11.mp4 222.9 MB
13. Constrained optimization/1. The theory for this section.mp4 218.8 MB
10. Min-max problems, best approximations, and least squares/3. Min-max, Problem 2.mp4 217.8 MB
8. Norm, distance, angles, and orthogonality in inner product spaces/21. Generalized Theorem of Pythagoras, Problem 8.mp4 217.4 MB
7. Inner product as a generalization of dot product/11. Positive definite matrices.mp4 214.1 MB
11. Diagonalization of symmetric matrices/19. Three tests for definiteness of symmetric matrices, Problem 10.mp4 213.7 MB
7. Inner product as a generalization of dot product/17. Gram matrix for an inner product in the space Pn of polynomials.mp4 207.4 MB
9. Projections and Gram–Schmidt process in various inner product spaces/12. Gram-Schmidt in IP spaces, Problem 6 Legendre polynomials.mp4 203.0 MB
2. Geometrical operators in the plane and in the 3-space/3. Problem 1 Line symmetry in the plane.mp4 202.5 MB
14. The Grand Finale Singular Value Decomposition and Pseudoinverses/8. SVD, Problem 2.mp4 197.4 MB
2. Geometrical operators in the plane and in the 3-space/4. Problem 2 Projection in the plane.mp4 196.3 MB
1. Introduction/1. Introduction.mp4 194.3 MB
6. Solving systems of linear ODE, and solving higher order ODE/9. How to deal with higher order linear ODE.mp4 191.3 MB
5. Recurrence relations, dynamical systems, Markov matrices/6. Systems of difference equations, Problem 3.mp4 187.5 MB
10. Min-max problems, best approximations, and least squares/10. Shortest distance from a subspace.mp4 186.8 MB
8. Norm, distance, angles, and orthogonality in inner product spaces/1. Norm in inner product spaces.mp4 181.8 MB
7. Inner product as a generalization of dot product/22. Inner product in the space of matrices, Problem 6.mp4 178.7 MB
12. Quadratic forms and their classification/16. Some nice visuals on quadratic surfaces.mp4 172.6 MB
10. Min-max problems, best approximations, and least squares/4. Min-max, Problem 3.mp4 171.9 MB
5. Recurrence relations, dynamical systems, Markov matrices/14. Markov matrices, Problem 9, Migration.mp4 171.4 MB
4. Intermezzo isomorphic vector spaces/10. Vector spaces, fields, rings; ring homomorphisms and isomorphisms.mp4 163.8 MB
4. Intermezzo isomorphic vector spaces/8. Isomorphic spaces Problem 2.mp4 163.8 MB
10. Min-max problems, best approximations, and least squares/20. Least squares, fitting a quadratic curve to data, Problem 13.mp4 160.2 MB
5. Recurrence relations, dynamical systems, Markov matrices/2. Two famous examples of recurrence.mp4 158.8 MB
14. The Grand Finale Singular Value Decomposition and Pseudoinverses/4. New facts about AT A eigenvalues and eigenvectors Singular values of A.mp4 155.4 MB
7. Inner product as a generalization of dot product/18. Two inner products on the space of polynomials Pn.mp4 150.2 MB
7. Inner product as a generalization of dot product/16. Inner product in the space of continuous functions.mp4 150.1 MB
11. Diagonalization of symmetric matrices/11. Spectral decomposition for symmetric matrices, Problem 3.mp4 149.1 MB
9. Projections and Gram–Schmidt process in various inner product spaces/6. Orthogonal sets are linearly independent, Problem 3.mp4 146.3 MB
12. Quadratic forms and their classification/2. Completing the square is not unique.mp4 145.8 MB
9. Projections and Gram–Schmidt process in various inner product spaces/8. Projections and orthogonal decomposition in IP spaces.mp4 141.1 MB
2. Geometrical operators in the plane and in the 3-space/8. Another formulation of eigendecomposition Spectral decomposition.mp4 140.5 MB
2. Geometrical operators in the plane and in the 3-space/11. Spectral decomposition, Problem 7.mp4 139.5 MB
12. Quadratic forms and their classification/20. Law of inertia for quadratic forms; Signature of a form, Problem 11.mp4 138.3 MB
8. Norm, distance, angles, and orthogonality in inner product spaces/4. Norm in the space of functions, Problem 2.mp4 136.3 MB
6. Solving systems of linear ODE, and solving higher order ODE/3. Systems of first order linear ODE with constant coefficients.mp4 136.1 MB
4. Intermezzo isomorphic vector spaces/1. You wouldn’t see the difference.mp4 136.0 MB
14. The Grand Finale Singular Value Decomposition and Pseudoinverses/10. Least squares, SVD, and pseudoinverse (Moore-Penrose inverse).mp4 134.6 MB
7. Inner product as a generalization of dot product/6. Euclidean n-space.mp4 132.8 MB
10. Min-max problems, best approximations, and least squares/7. Another look at orthogonal projections as matrix transformations.mp4 132.8 MB
6. Solving systems of linear ODE, and solving higher order ODE/6. System of ODE, Problem 1.mp4 129.6 MB
8. Norm, distance, angles, and orthogonality in inner product spaces/22. Generalized Theorem of Pythagoras, Problem 9.mp4 128.6 MB
12. Quadratic forms and their classification/9. Principal axes; The shortest distance from the origin, Problem 3.mp4 127.8 MB
2. Geometrical operators in the plane and in the 3-space/1. Eigendecomposition, recap.mp4 125.9 MB
11. Diagonalization of symmetric matrices/13. Orthogonal diagonalization, Problem 5.mp4 121.5 MB
8. Norm, distance, angles, and orthogonality in inner product spaces/3. Frobenius norm of matrices, Problem 1.mp4 117.6 MB
10. Min-max problems, best approximations, and least squares/16. Four fundamental matrix spaces and the normal equation.mp4 117.0 MB
8. Norm, distance, angles, and orthogonality in inner product spaces/6. Frobenius distance between matrices, Problem 3.mp4 115.6 MB
9. Projections and Gram–Schmidt process in various inner product spaces/3. Why does normalizing work in the same way in all IP spaces.mp4 115.0 MB
2. Geometrical operators in the plane and in the 3-space/9. Powers of matrices Two methods.mp4 114.8 MB
8. Norm, distance, angles, and orthogonality in inner product spaces/17. Orthogonality in inner product spaces, Problem 7.mp4 109.1 MB
12. Quadratic forms and their classification/8. Quadratic curves by distances; shortest distance from the origin.mp4 107.3 MB
8. Norm, distance, angles, and orthogonality in inner product spaces/20. Generalized Theorem of Pythagoras.mp4 107.0 MB
7. Inner product as a generalization of dot product/23. Frobenius inner product; Hadamard product of matrices.mp4 106.9 MB
12. Quadratic forms and their classification/15. Generally about quadratic surfaces.mp4 106.8 MB
11. Diagonalization of symmetric matrices/15. Orthogonal diagonalization, Problem 7.mp4 105.5 MB
8. Norm, distance, angles, and orthogonality in inner product spaces/5. Distance in inner product spaces.mp4 100.7 MB
11. Diagonalization of symmetric matrices/8. The Spectral Theorem Each symmetric matrix is orthogonally diagonalizable.mp4 100.4 MB
11. Diagonalization of symmetric matrices/3. Eigenvectors corresponding to distinct eigenvalues for a symmetric matrix.mp4 99.4 MB
5. Recurrence relations, dynamical systems, Markov matrices/3. Linear discrete dynamical systems.mp4 88.2 MB
4. Intermezzo isomorphic vector spaces/6. Why you don’t see the difference.mp4 88.0 MB
11. Diagonalization of symmetric matrices/16. Spectral decomposition, Problem 8.mp4 87.3 MB
2. Geometrical operators in the plane and in the 3-space/10. Spectral decomposition, Problem 6.mp4 85.3 MB
6. Solving systems of linear ODE, and solving higher order ODE/4. A very simple example.mp4 81.7 MB
4. Intermezzo isomorphic vector spaces/2. Different spaces with the same structure.mp4 80.8 MB
6. Solving systems of linear ODE, and solving higher order ODE/1. What is an ODE and what kinds of ODE we are going to deal with.mp4 78.0 MB
10. Min-max problems, best approximations, and least squares/12. Shortest distance, Problem 9.mp4 77.4 MB
10. Min-max problems, best approximations, and least squares/1. In this section.mp4 74.1 MB
5. Recurrence relations, dynamical systems, Markov matrices/1. Continuous versus discrete.mp4 73.5 MB
2. Geometrical operators in the plane and in the 3-space/2. Eigendecomposition and operators.mp4 73.3 MB
12. Quadratic forms and their classification/21. Four methods of determining definiteness; Problem 12.mp4 73.1 MB
15. Wrap-up Linear Algebra and Geometry/2. So, what’s next.mp4 72.9 MB
12. Quadratic forms and their classification/7. Quadratic curves as conic sections.mp4 71.3 MB
14. The Grand Finale Singular Value Decomposition and Pseudoinverses/2. Why do we need SVD.mp4 70.9 MB
14. The Grand Finale Singular Value Decomposition and Pseudoinverses/3. We know really a lot about AT A for any rectangular matrix A.mp4 68.4 MB
5. Recurrence relations, dynamical systems, Markov matrices/10. Markov matrices.mp4 67.4 MB
12. Quadratic forms and their classification/3. What kind of questions we want to answer.mp4 66.8 MB
12. Quadratic forms and their classification/10. Classification of quadratic forms in two variables.mp4 64.9 MB
14. The Grand Finale Singular Value Decomposition and Pseudoinverses/12. SVD and Fundamental Theorem of Linear Algebra.mp4 64.6 MB
8. Norm, distance, angles, and orthogonality in inner product spaces/18. What is triangle inequality.mp4 64.3 MB
12. Quadratic forms and their classification/4. 163 Quadratic forms in two variables, Problem 1..mp4 63.0 MB
11. Diagonalization of symmetric matrices/4. Complex numbers a brief repetition.mp4 62.8 MB
6. Solving systems of linear ODE, and solving higher order ODE/2. Solutions to first order linear ODE with constant coefficients.mp4 62.3 MB
8. Norm, distance, angles, and orthogonality in inner product spaces/16. Orthogonality in inner product spaces depends on inner product.mp4 61.5 MB
11. Diagonalization of symmetric matrices/6. Orthogonal diagonalization.mp4 61.3 MB
11. Diagonalization of symmetric matrices/20. Symmetric square roots of symmetric positive definite matrices; singular values.mp4 61.0 MB
7. Inner product as a generalization of dot product/21. Inner product in the space of square matrices.mp4 60.6 MB
6. Solving systems of linear ODE, and solving higher order ODE/7. System of ODE, Problem 2.mp4 60.1 MB
7. Inner product as a generalization of dot product/15. Gram matrix, Problem 4.mp4 57.9 MB
8. Norm, distance, angles, and orthogonality in inner product spaces/13. More weird geometry Angles in inner product spaces, Problem 5.mp4 55.5 MB
11. Diagonalization of symmetric matrices/18. The wonderful strength of an orthogonally diagonalized matrix.mp4 54.5 MB
9. Projections and Gram–Schmidt process in various inner product spaces/11. Gram-Schmidt in IP spaces.mp4 54.5 MB
12. Quadratic forms and their classification/5. Quadratic forms in two variables, Problem 2.mp4 54.3 MB
7. Inner product as a generalization of dot product/2. Dot product in Part 1.mp4 54.2 MB
10. Min-max problems, best approximations, and least squares/8. Orthogonal projections, Problem 6.mp4 53.2 MB
8. Norm, distance, angles, and orthogonality in inner product spaces/2. Weird geometry in the Euclidean space with weighted inner product.mp4 49.8 MB
7. Inner product as a generalization of dot product/3. Dot product and orthogonality in Part 2.mp4 49.6 MB
14. The Grand Finale Singular Value Decomposition and Pseudoinverses/1. All our roads led us to SVD.mp4 49.2 MB
9. Projections and Gram–Schmidt process in various inner product spaces/1. Different but still awesome!.mp4 48.1 MB
8. Norm, distance, angles, and orthogonality in inner product spaces/8. First step to defining abstract angles.mp4 47.5 MB
11. Diagonalization of symmetric matrices/10. Orthogonal diagonalization, Problem 2.mp4 46.6 MB
10. Min-max problems, best approximations, and least squares/13. Shortest distance, Problem 10.mp4 46.2 MB
8. Norm, distance, angles, and orthogonality in inner product spaces/12. Angles in inner product spaces.mp4 45.5 MB
12. Quadratic forms and their classification/6. Quadratic curves, generally.mp4 45.4 MB
7. Inner product as a generalization of dot product/4. From R^2 to inner product spaces.mp4 44.8 MB
13. Constrained optimization/3. Constrained optimization, Problem 2.mp4 44.5 MB
10. Min-max problems, best approximations, and least squares/15. Least squares solution and residual vector.mp4 44.0 MB
13. Constrained optimization/2. Constrained optimization, Problem 1.mp4 43.5 MB
11. Diagonalization of symmetric matrices/2. Some properties of symmetric matrices.mp4 42.2 MB
10. Min-max problems, best approximations, and least squares/14. Solvability of systems of equations in terms of the column space.mp4 40.8 MB
7. Inner product as a generalization of dot product/20. Inner product in the space of m × n matrices.mp4 40.4 MB
4. Intermezzo isomorphic vector spaces/5. A necessary and sufficient condition for isomorphic vector spaces.mp4 39.9 MB
1. Introduction/1.2 Slides Introduction to the course.pdf 39.4 MB
7. Inner product as a generalization of dot product/7. A very important remark about notation.mp4 38.3 MB
8. Norm, distance, angles, and orthogonality in inner product spaces/7. Distance in the space of functions, Problem 4.mp4 37.3 MB
11. Diagonalization of symmetric matrices/9. Orthogonal diagonalization how to do it.mp4 36.6 MB
9. Projections and Gram–Schmidt process in various inner product spaces/7. Coordinates in orthogonal bases in IP spaces.mp4 35.6 MB
4. Intermezzo isomorphic vector spaces/7. Isomorphic spaces Problem 1.mp4 35.5 MB
10. Min-max problems, best approximations, and least squares/11. Shortest distance, Problem 8.mp4 35.3 MB
7. Inner product as a generalization of dot product/8. Inner and outer products.mp4 34.1 MB
8. Norm, distance, angles, and orthogonality in inner product spaces/14. Angles in inner product spaces, Problem 6.mp4 34.0 MB
5. Recurrence relations, dynamical systems, Markov matrices/11. Each Markov matrix has eigenvalue 1.mp4 33.0 MB
4. Intermezzo isomorphic vector spaces/3. More examples of isomorphic vector spaces.mp4 32.5 MB
7. Inner product as a generalization of dot product/1. Between concrete and abstract.mp4 30.3 MB
10. Min-max problems, best approximations, and least squares/9. Orthogonal projections, Problem 7.mp4 30.1 MB
11. Diagonalization of symmetric matrices/7. If a matrix is orthogonally diagonalizable, it is symmetric.mp4 29.8 MB
5. Recurrence relations, dynamical systems, Markov matrices/17. Where to read more on this topic.mp4 28.7 MB
9. Projections and Gram–Schmidt process in various inner product spaces/2. ON bases in IP spaces.mp4 28.6 MB
13. Constrained optimization/4. Constrained optimization, Problem 3.mp4 27.2 MB
8. Norm, distance, angles, and orthogonality in inner product spaces/15. Orthogonality in inner product spaces.mp4 27.2 MB
15. Wrap-up Linear Algebra and Geometry/1. Linear Algebra and Geometry, Wrap-up.mp4 26.8 MB
7. Inner product as a generalization of dot product/10. Remember transposed matrices.mp4 23.5 MB
15. Wrap-up Linear Algebra and Geometry/3. Final words.mp4 23.4 MB
13. Constrained optimization/5. Constrained optimization, Problem 4.mp4 21.3 MB
8. Norm, distance, angles, and orthogonality in inner product spaces/11. Cauchy-Schwarz inequality in the space of continuous functions.mp4 19.7 MB
6. Solving systems of linear ODE, and solving higher order ODE/10.4 Slides Another way of looking at the same problem.pdf 13.4 MB
4. Intermezzo isomorphic vector spaces/1.1 Slides You would not see the difference.pdf 9.6 MB
3. More problem solving; spaces different from R^n/1.1 Notes Eigendecomposition Problem 1.pdf 9.1 MB
7. Inner product as a generalization of dot product/14.1 Notes Gram matrix.pdf 8.7 MB
11. Diagonalization of symmetric matrices/3.1 Slides_Eigenvectors corresponding to distinct eigenvalues for a symmetric matrix are orthogonal.pdf 8.4 MB
11. Diagonalization of symmetric matrices/1.2 Slides_The link between symmetric matrices and quadratic forms Problem 1.pdf 8.2 MB
12. Quadratic forms and their classification/20.1 Slides_Law of inertia for quadratic forms; Signature of a form Problem 11.pdf 8.1 MB
10. Min-max problems, best approximations, and least squares/13.1 Slides_Shortest distance Problem 10.pdf 7.6 MB
7. Inner product as a generalization of dot product/21.1 Slides Inner products in the space of square matrices.pdf 7.6 MB
3. More problem solving; spaces different from R^n/5.1 Notes In the space of polynomials Problem 5.pdf 7.1 MB
4. Intermezzo isomorphic vector spaces/12.1 Notes Vector spaces Fields Rings Problem 5.pdf 6.4 MB
10. Min-max problems, best approximations, and least squares/7.1 Slides_Another look at orthogonal projections as matrix transformations.pdf 6.4 MB
3. More problem solving; spaces different from R^n/4.1 Notes Powers and roots Problem 4.pdf 6.4 MB
2. Geometrical operators in the plane and in the 3-space/8.1 Slides Another formulation of eigendecomposition Spectral.pdf 6.2 MB
11. Diagonalization of symmetric matrices/16.1 Slides_Spectral decomposition Problem 8.pdf 6.2 MB
6. Solving systems of linear ODE, and solving higher order ODE/3.1 Slides Systems of first order linear ODE with constant coefficients.pdf 6.1 MB
11. Diagonalization of symmetric matrices/14.1 Notes_Orthogonal diagonalization Problem 6.pdf 5.9 MB
8. Norm, distance, angles, and orthogonality in inner product spaces/14.1 Slides_Angles in inner product spaces Problem 6.pdf 5.8 MB
3. More problem solving; spaces different from R^n/6.2 Slides In the space of polynomials Problem 6.pdf 5.7 MB
8. Norm, distance, angles, and orthogonality in inner product spaces/9.1 Notes_Cauchy--Schwarz inequality Proof 1.pdf 5.6 MB
7. Inner product as a generalization of dot product/13.1 Notes Matrix inner product on Rn.pdf 5.6 MB
12. Quadratic forms and their classification/19.1 Notes_Quadratic surfaces Problem 10.pdf 5.5 MB
3. More problem solving; spaces different from R^n/7.1 Notes In the space of matrices Problem 7.pdf 5.5 MB
6. Solving systems of linear ODE, and solving higher order ODE/5.2 Slides The method.pdf 5.4 MB
14. The Grand Finale Singular Value Decomposition and Pseudoinverses/5.1 Notes_ON bases containing only eigenvectors of certain matrix products.pdf 5.4 MB
3. More problem solving; spaces different from R^n/2.1 Notes Eigendecomposition Problem 2.pdf 5.4 MB
2. Geometrical operators in the plane and in the 3-space/9.1 Slides Powers of matrices Two methods.pdf 5.4 MB
9. Projections and Gram–Schmidt process in various inner product spaces/4.2 Notes_Orthonormal sets of continuous functions Problem 1.pdf 5.4 MB
12. Quadratic forms and their classification/1.1 Notes_The correspondence between quadratic forms and symmetric matrices is 1to1.pdf 5.4 MB
12. Quadratic forms and their classification/14.2 Slides_Classification of curves Problem 7.pdf 5.3 MB
12. Quadratic forms and their classification/10.1 Slides_Classification of quadratic forms in two variables.pdf 5.2 MB
2. Geometrical operators in the plane and in the 3-space/7.1 Notes Problem 5 Projection in the 3 space.pdf 5.2 MB
2. Geometrical operators in the plane and in the 3-space/11.1 Slides Spectral decomposition Problem 7.pdf 5.2 MB
6. Solving systems of linear ODE, and solving higher order ODE/8.1 Notes System of ODE Problem 3.pdf 5.1 MB
3. More problem solving; spaces different from R^n/3.1 Notes Powers and roots Problem 3.pdf 5.0 MB
5. Recurrence relations, dynamical systems, Markov matrices/4.1 Notes Systems of difference equations Problem 1.pdf 5.0 MB
14. The Grand Finale Singular Value Decomposition and Pseudoinverses/6.2 Slides_Singular value decomposition with proof and geometric interpretation.pdf 5.0 MB
2. Geometrical operators in the plane and in the 3-space/12.2 Slides Spectral decomposition Geometrical illustration.pdf 5.0 MB
11. Diagonalization of symmetric matrices/12.1 Notes_Orthogonal diagonalization Problem 4.pdf 5.0 MB
4. Intermezzo isomorphic vector spaces/7.1 Slides Isomorphic spaces Problem 1.pdf 4.9 MB
5. Recurrence relations, dynamical systems, Markov matrices/13.1 Notes Markov matrices Problem 8 Restaurant.pdf 4.9 MB
11. Diagonalization of symmetric matrices/5.1 Notes_Eigenvalues for a (real) symmetric matrix are real.pdf 4.9 MB
11. Diagonalization of symmetric matrices/19.1 Notes_Three tests for definiteness of symmetric matrices Problem 10.pdf 4.6 MB
2. Geometrical operators in the plane and in the 3-space/10.1 Slides Spectral decomposition Problem 6.pdf 4.5 MB
14. The Grand Finale Singular Value Decomposition and Pseudoinverses/9.1 Notes_More new facts about ATA Six equivalent statements.pdf 4.3 MB
11. Diagonalization of symmetric matrices/11.1 Slides_Spectral decomposition for symmetric matrices Problem 3.pdf 4.3 MB
4. Intermezzo isomorphic vector spaces/4.1 Notes A necessary condition for isomorphic vector spaces.pdf 4.3 MB
2. Geometrical operators in the plane and in the 3-space/1.1 Slides Eigendecomposition recap.pdf 4.3 MB
11. Diagonalization of symmetric matrices/6.1 Slides_Orthogonal diagonalization.pdf 4.1 MB
12. Quadratic forms and their classification/17.1 Notes_Quadratic surfaces Shortest distance Problem 8.pdf 4.1 MB
12. Quadratic forms and their classification/21.2 Slides_Four methods of determining definiteness Problem 12.pdf 4.1 MB
14. The Grand Finale Singular Value Decomposition and Pseudoinverses/7.1 Notes_SVD, reduced singular value decomposition Problem 1.pdf 4.1 MB
14. The Grand Finale Singular Value Decomposition and Pseudoinverses/6.1 Notes_Singular value decomposition with proof and geometric interpretation.pdf 4.0 MB
4. Intermezzo isomorphic vector spaces/11.1 Notes Vector spaces Fields Rings Problem 4.pdf 4.0 MB
7. Inner product as a generalization of dot product/5.1 Notes Inner product spaces.pdf 4.0 MB
13. Constrained optimization/1.1 Slides_The theory for this section.pdf 4.0 MB
10. Min-max problems, best approximations, and least squares/5.1 Notes_Min max Problem 4.pdf 4.0 MB
4. Intermezzo isomorphic vector spaces/9.1 Notes Isomorphic spaces Problem 3.pdf 3.9 MB
10. Min-max problems, best approximations, and least squares/17.1 Notes_Least squares Problem 11 by normal equation.pdf 3.9 MB
9. Projections and Gram–Schmidt process in various inner product spaces/13.1 Notes_Gram Schmidt in IP spaces Problem 7.pdf 3.8 MB
7. Inner product as a generalization of dot product/12.1 Notes Quadratic forms and how to read them.pdf 3.8 MB
9. Projections and Gram–Schmidt process in various inner product spaces/10.1 Notes_Projections and orthogonal decomposition in IP spaces Problem 5.pdf 3.7 MB
10. Min-max problems, best approximations, and least squares/2.1 Notes_Min max Problem 1.pdf 3.7 MB
14. The Grand Finale Singular Value Decomposition and Pseudoinverses/4.3 Slides_New facts about ATA eigenvalues and eigenvectors Singular values of A.pdf 3.6 MB
8. Norm, distance, angles, and orthogonality in inner product spaces/23.1 Notes_Generalized Theorem of Pythagoras Problem 10.pdf 3.6 MB
10. Min-max problems, best approximations, and least squares/18.1 Notes_Least squares Problem 11 by projection.pdf 3.6 MB
10. Min-max problems, best approximations, and least squares/3.1 Notes_Min max Problem 2.pdf 3.6 MB
5. Recurrence relations, dynamical systems, Markov matrices/7.1 Notes Higher order difference equations Problem 4.pdf 3.6 MB
12. Quadratic forms and their classification/13.2 Slides_Different roles of symmetric matrices Problem 6.pdf 3.6 MB
10. Min-max problems, best approximations, and least squares/20.1 Notes_Least squares Fitting a quadratic curve to data Problem 13.pdf 3.6 MB
5. Recurrence relations, dynamical systems, Markov matrices/16.1 Notes Dynamical systems Problem 11.pdf 3.6 MB
7. Inner product as a generalization of dot product/22.1 Notes Inner product in the space of matrices Problem 6.pdf 3.6 MB
10. Min-max problems, best approximations, and least squares/12.1 Slides_Shortest distance Problem 9.pdf 3.5 MB
7. Inner product as a generalization of dot product/17.1 Slides Gram matrix for an inner product in the space P_n of polynomials.pdf 3.3 MB
8. Norm, distance, angles, and orthogonality in inner product spaces/19.1 Notes_Triangle inequality in inner product spaces.pdf 3.1 MB
12. Quadratic forms and their classification/9.1 Slides_Principal axes Shortest distance Problem 3.pdf 3.0 MB
7. Inner product as a generalization of dot product/9.1 Notes Weighted Euclidean inner product Problem 1.pdf 3.0 MB
9. Projections and Gram–Schmidt process in various inner product spaces/9.1 Notes_Projections and orthogonal decomposition in IP spaces Problem 4.pdf 3.0 MB
13. Constrained optimization/3.1 Slides_Constrained optimization Problem 2.pdf 3.0 MB
10. Min-max problems, best approximations, and least squares/1.1 Slides_In this section.pdf 2.9 MB
8. Norm, distance, angles, and orthogonality in inner product spaces/10.1 Notes_Cauchy--Schwarz inequality Proof 2.pdf 2.9 MB
11. Diagonalization of symmetric matrices/17.2 Notes_Positive and negative definite matrices semidefinite and indefinite matrices Problem 9.pdf 2.9 MB
13. Constrained optimization/2.1 Slides_Constrained optimization Problem 1.pdf 2.8 MB
14. The Grand Finale Singular Value Decomposition and Pseudoinverses/11.1 Notes_Pseudoinverse Problem 3.pdf 2.8 MB
6. Solving systems of linear ODE, and solving higher order ODE/10.3 Notes Another way of looking at the same problem.pdf 2.8 MB
5. Recurrence relations, dynamical systems, Markov matrices/5.1 Notes Systems of difference equations Problem 2.pdf 2.8 MB
5. Recurrence relations, dynamical systems, Markov matrices/9.1 Notes Higher order difference equations Problem 6.pdf 2.8 MB
10. Min-max problems, best approximations, and least squares/6.1 Notes_Min max Problem 5.pdf 2.8 MB
6. Solving systems of linear ODE, and solving higher order ODE/4.1 Slides A very simple example.pdf 2.8 MB
6. Solving systems of linear ODE, and solving higher order ODE/5.1 Notes The method.pdf 2.8 MB
12. Quadratic forms and their classification/5.1 Slides_Quadratic forms in two variables Problem 2.pdf 2.7 MB
7. Inner product as a generalization of dot product/16.1 Notes Inner product in the space of continuous functions.pdf 2.7 MB
10. Min-max problems, best approximations, and least squares/2.2 Slides_Min max Problem 1.pdf 2.7 MB
12. Quadratic forms and their classification/18.1 Notes_Quadratic surfaces Problem 9.pdf 2.7 MB
5. Recurrence relations, dynamical systems, Markov matrices/15.1 Notes Markov matrices Problem 10 Election.pdf 2.7 MB
12. Quadratic forms and their classification/13.1 Notes_Different roles of symmetric matrices Problem 6.pdf 2.7 MB
2. Geometrical operators in the plane and in the 3-space/12.1 Notes Spectral decomposition Geometrical illustration.pdf 2.6 MB
10. Min-max problems, best approximations, and least squares/19.1 Notes_Least squares Fitting a line Problem 12.pdf 2.6 MB
7. Inner product as a generalization of dot product/19.1 Notes The evaluation inner products on P2 Problem 5.pdf 2.6 MB
5. Recurrence relations, dynamical systems, Markov matrices/12.1 Notes Steady state vector Equilibrium vector Problem 7.pdf 2.6 MB
5. Recurrence relations, dynamical systems, Markov matrices/8.1 Notes Higher order difference equations Problem 5.pdf 2.6 MB
11. Diagonalization of symmetric matrices/10.1 Slides_Orthogonal diagonalization Problem 2.pdf 2.6 MB
12. Quadratic forms and their classification/11.1 Notes_Classification of curves Problem 4.pdf 2.5 MB
11. Diagonalization of symmetric matrices/20.1 Slides_Symmetric square roots of symmetric positive definite matrices Singular values Problem 11.pdf 2.5 MB
6. Solving systems of linear ODE, and solving higher order ODE/6.1 Slides System of ODE Problem 1.pdf 2.5 MB
4. Intermezzo isomorphic vector spaces/8.1 Notes Isomorphic spaces Problem 2.pdf 2.5 MB
8. Norm, distance, angles, and orthogonality in inner product spaces/16.1 Slides_Orthogonality in inner product spaces depends on inner product.pdf 2.5 MB
11. Diagonalization of symmetric matrices/1.1 Notes_The link between symmetric matrices and quadratic forms Problem 1.pdf 2.5 MB
14. The Grand Finale Singular Value Decomposition and Pseudoinverses/8.1 Notes_SVD Problem 2.pdf 2.4 MB
9. Projections and Gram–Schmidt process in various inner product spaces/12.1 Notes_Gram Schmidt in IP spaces Problem 6 Legendre polynomials.pdf 2.4 MB
8. Norm, distance, angles, and orthogonality in inner product spaces/5.1 Notes_Distance in inner product spaces.pdf 2.4 MB
11. Diagonalization of symmetric matrices/5.2 Slides_Eigenvalues for a (real) symmetric matrix are real.pdf 2.4 MB
6. Solving systems of linear ODE, and solving higher order ODE/7.1 Slides System of ODE Problem 2.pdf 2.4 MB
8. Norm, distance, angles, and orthogonality in inner product spaces/22.1 Notes_Generalized Theorem of Pythagoras Problem 9.pdf 2.3 MB
14. The Grand Finale Singular Value Decomposition and Pseudoinverses/10.1 Slides_Least squares, SVD, and pseudoinverse Moore Penrose inverse.pdf 2.3 MB
7. Inner product as a generalization of dot product/2.1 Slides Dot product in Part 1.pdf 2.3 MB
11. Diagonalization of symmetric matrices/19.2 Slides_Three tests for definiteness of symmetric matrices Problem 10.pdf 2.3 MB
7. Inner product as a generalization of dot product/15.1 Slides Gram matrix Problem 4.pdf 2.3 MB
9. Projections and Gram–Schmidt process in various inner product spaces/1.1 Slides_Different but still awesome.pdf 2.3 MB
12. Quadratic forms and their classification/15.1 Slides_Generally about quadratic surfaces.pdf 2.2 MB
2. Geometrical operators in the plane and in the 3-space/6.1 Notes Problem 4 Projection in the 3 space.pdf 2.2 MB
13. Constrained optimization/4.1 Slides_Constrained optimization Problem 3.pdf 2.1 MB
8. Norm, distance, angles, and orthogonality in inner product spaces/22.2 Slides_Generalized Theorem of Pythagoras Problem 9.pdf 2.0 MB
6. Solving systems of linear ODE, and solving higher order ODE/10.1 Article-Solved-Problems-Eigenvalues-ODE.pdf 2.0 MB
11. Diagonalization of symmetric matrices/18.1 Slides_The wonderful strength of an orthogonally diagonalized matrix.pdf 2.0 MB
7. Inner product as a generalization of dot product/3.1 Slides Dot product and orthogonality in Part 2.pdf 2.0 MB
6. Solving systems of linear ODE, and solving higher order ODE/9.3 Slides How to deal with higher order linear ODE.pdf 2.0 MB
8. Norm, distance, angles, and orthogonality in inner product spaces/19.2 Slides_Triangle inequality in inner product spaces.pdf 1.9 MB
9. Projections and Gram–Schmidt process in various inner product spaces/12.2 Slides_Gram Schmidt in IP spaces Problem 6 Legendre polynomials.pdf 1.9 MB
14. The Grand Finale Singular Value Decomposition and Pseudoinverses/9.2 Slides_More new facts about ATA Six equivalent statements.pdf 1.9 MB
11. Diagonalization of symmetric matrices/17.3 Slides_Positive and negative definite matrices semidefinite and indefinite matrices Problem 9.pdf 1.8 MB
5. Recurrence relations, dynamical systems, Markov matrices/4.2 Slides Systems of difference equations Problem 1.pdf 1.7 MB
7. Inner product as a generalization of dot product/23.1 Slides_Frobenius inner product and Hadamard product of matrices.pdf 1.7 MB
6. Solving systems of linear ODE, and solving higher order ODE/2.1 Slides Solutions to first order linear ODE with constant coefficients.pdf 1.6 MB
10. Min-max problems, best approximations, and least squares/10.1 Notes_Shortest distance from a subspace.pdf 1.6 MB
15. Wrap-up Linear Algebra and Geometry/1.1 Slides_Linear Algebra and Geometry Wrap up.pdf 1.6 MB
7. Inner product as a generalization of dot product/11.1 Notes Positive definite matrices.pdf 1.6 MB
12. Quadratic forms and their classification/8.1 Slides_Quadratic curves by distances Shortest distance from the origin.pdf 1.6 MB
14. The Grand Finale Singular Value Decomposition and Pseudoinverses/8.2 Slides_SVD Problem 2.pdf 1.5 MB
7. Inner product as a generalization of dot product/18.1 Notes Two inner products in the space of polynomials.pdf 1.5 MB
3. More problem solving; spaces different from R^n/6.1 Notes In the space of polynomials Problem 6.pdf 1.5 MB
7. Inner product as a generalization of dot product/6.1 Notes Euclidean n-space.pdf 1.5 MB
7. Inner product as a generalization of dot product/10.1 Slides Remember transposed matrices.pdf 1.5 MB
7. Inner product as a generalization of dot product/13.2 Slides Matrix inner product on Rn.pdf 1.5 MB
12. Quadratic forms and their classification/1.2 Slides_The correspondence between quadratic forms and symmetric matrices is 1to1.pdf 1.5 MB
5. Recurrence relations, dynamical systems, Markov matrices/17.1 Slides Where to read more on this topic.pdf 1.5 MB
5. Recurrence relations, dynamical systems, Markov matrices/2.1 Notes Two famous examples of recurrence.pdf 1.5 MB
10. Min-max problems, best approximations, and least squares/4.1 Notes_Min max Problem 3.pdf 1.4 MB
9. Projections and Gram–Schmidt process in various inner product spaces/8.1 Notes_Projections and orthogonal decomposition in IP spaces.pdf 1.4 MB
5. Recurrence relations, dynamical systems, Markov matrices/14.1 Notes Markov matrices Problem 9 Migration.pdf 1.4 MB
11. Diagonalization of symmetric matrices/15.1 Notes_Orthogonal diagonalization Problem 7.pdf 1.4 MB
2. Geometrical operators in the plane and in the 3-space/5.1 Notes Problem 3 Symmetry in the 3 space.pdf 1.4 MB
7. Inner product as a generalization of dot product/11.2 Slides Positive definite matrices.pdf 1.4 MB
9. Projections and Gram–Schmidt process in various inner product spaces/5.1 Notes_Orthogonal complements Problem 2.pdf 1.4 MB
8. Norm, distance, angles, and orthogonality in inner product spaces/21.1 Notes_Generalized Theorem of Pythagoras Problem 8.pdf 1.4 MB
8. Norm, distance, angles, and orthogonality in inner product spaces/1.1 Notes_Norm in inner product spaces.pdf 1.4 MB
2. Geometrical operators in the plane and in the 3-space/3.2 Slides Problem 1 Line symmetry in the plane.pdf 1.4 MB
12. Quadratic forms and their classification/12.1 Notes_Classification of curves Problem 5.pdf 1.3 MB
9. Projections and Gram–Schmidt process in various inner product spaces/3.1 Notes_Why does normalizing work in the same way in all IP spaces.pdf 1.3 MB
6. Solving systems of linear ODE, and solving higher order ODE/9.2 Notes How to deal with higher order linear ODE.pdf 1.3 MB
8. Norm, distance, angles, and orthogonality in inner product spaces/13.1 Slides_More weird geometry Angles in inner product spaces Problem 5.pdf 1.3 MB
14. The Grand Finale Singular Value Decomposition and Pseudoinverses/4.2 Notes_New facts about ATA eigenvalues and eigenvectors Singular values of A.pdf 1.3 MB
11. Diagonalization of symmetric matrices/13.1 Notes_Orthogonal diagonalization Problem 5.pdf 1.3 MB
9. Projections and Gram–Schmidt process in various inner product spaces/6.1 Notes_Orthogonal sets are linearly independent Problem 3.pdf 1.3 MB
5. Recurrence relations, dynamical systems, Markov matrices/6.1 Notes Systems of difference equations Problem 3.pdf 1.3 MB
7. Inner product as a generalization of dot product/14.2 Slides Gram matrix.pdf 1.3 MB
10. Min-max problems, best approximations, and least squares/16.1 Slides_Four fundamental matrix spaces and the normal equation.pdf 1.3 MB
5. Recurrence relations, dynamical systems, Markov matrices/12.2 Slides Steady state vector Equilibrium vector Problem 7.pdf 1.3 MB
12. Quadratic forms and their classification/2.1 Notes_Completing the square is not unique.pdf 1.3 MB
8. Norm, distance, angles, and orthogonality in inner product spaces/17.1 Notes_Orthogonality in inner product spaces Problem 7.pdf 1.3 MB
2. Geometrical operators in the plane and in the 3-space/4.2 Slides Problem 2 Projection in the plane.pdf 1.3 MB
14. The Grand Finale Singular Value Decomposition and Pseudoinverses/12.1 Slides_SVD and Fundamental Theorem of Linear Algebra.pdf 1.3 MB
8. Norm, distance, angles, and orthogonality in inner product spaces/20.1 Notes_Generalized Theorem of Pythagoras.pdf 1.3 MB
12. Quadratic forms and their classification/14.1 Notes_Classification of curves Problem 7.pdf 1.3 MB
4. Intermezzo isomorphic vector spaces/10.1 Slides Vector spaces Fields Rings Ring isomorphisms.pdf 1.3 MB
6. Solving systems of linear ODE, and solving higher order ODE/1.1 Slides What is an ODE and what kinds of ODE we are going to deal with.pdf 1.3 MB
8. Norm, distance, angles, and orthogonality in inner product spaces/4.1 Notes_Norm in the space of functions Problem 2.pdf 1.2 MB
9. Projections and Gram–Schmidt process in various inner product spaces/14.3 Slides_Easy computations of IP in ON bases Problem 8.pdf 1.2 MB
6. Solving systems of linear ODE, and solving higher order ODE/9.1 Article-Supplement-to-Video-81-in-Part2-Non-homogenous-ODE.pdf 1.2 MB
9. Projections and Gram–Schmidt process in various inner product spaces/14.2 Notes_Easy computations of IP in ON bases Problem 8.pdf 1.2 MB
8. Norm, distance, angles, and orthogonality in inner product spaces/6.1 Notes_Frobenius distance between matrices Problem 3.pdf 1.2 MB
13. Constrained optimization/5.1 Slides_Constrained optimization Problem 4.pdf 1.2 MB
12. Quadratic forms and their classification/21.1 Article-Solved-Problems-Quadratic-Forms.pdf 1.2 MB
8. Norm, distance, angles, and orthogonality in inner product spaces/3.1 Notes_Frobenius norm of matrices Problem 1.pdf 1.2 MB
10. Min-max problems, best approximations, and least squares/11.1 Slides_Shortest distance Problem 8.pdf 1.1 MB
4. Intermezzo isomorphic vector spaces/4.2 Slides A necessary condition for isomorphic vector spaces.pdf 1.1 MB
8. Norm, distance, angles, and orthogonality in inner product spaces/7.1 Slides_Distance in the space of functions Problem 4.pdf 1.1 MB
9. Projections and Gram–Schmidt process in various inner product spaces/8.2 Slides_Projections and orthogonal decomposition in IP spaces.pdf 1.1 MB
3. More problem solving; spaces different from R^n/5.2 Slides In the space of polynomials Problem 5.pdf 1.0 MB
6. Solving systems of linear ODE, and solving higher order ODE/10.2 Article-Theory-Eigenvalues-ODE.pdf 998.9 kB
10. Min-max problems, best approximations, and least squares/8.1 Slides_Orthogonal projections Problem 6.pdf 997.5 kB
9. Projections and Gram–Schmidt process in various inner product spaces/11.1 Slides_Gram Schmidt in IP spaces.pdf 992.3 kB
9. Projections and Gram–Schmidt process in various inner product spaces/5.2 Slides_Orthogonal complements Problem 2.pdf 986.0 kB
4. Intermezzo isomorphic vector spaces/5.1 Slides A necessary and sufficient condition for isomorphic vector spaces.pdf 973.8 kB
11. Diagonalization of symmetric matrices/7.1 Slides_If a matrix is orthogonally diagonalizable it is symmetric.pdf 924.8 kB
14. The Grand Finale Singular Value Decomposition and Pseudoinverses/7.2 Slides_SVD, reduced singular value decomposition Problem 1.pdf 880.8 kB
12. Quadratic forms and their classification/16.1 Slides_Some nice visuals on quadratic surfaces.pdf 869.9 kB
14. The Grand Finale Singular Value Decomposition and Pseudoinverses/5.2 Slides_ON bases containing only eigenvectors of certain matrix products.pdf 856.5 kB
4. Intermezzo isomorphic vector spaces/11.2 Slides Vector spaces Fields Rings Problem 4.pdf 837.4 kB
14. The Grand Finale Singular Value Decomposition and Pseudoinverses/3.1 Slides_We know really a lot about ATA for any rectangular matrix A.pdf 835.3 kB
12. Quadratic forms and their classification/19.2 Slides_Quadratic surfaces Problem 10.pdf 809.2 kB
3. More problem solving; spaces different from R^n/3.2 Slides Powers and roots Problem 3.pdf 786.3 kB
10. Min-max problems, best approximations, and least squares/9.1 Slides_Orthogonal projections Problem 7.pdf 771.4 kB
8. Norm, distance, angles, and orthogonality in inner product spaces/23.2 Slides_Generalized Theorem of Pythagoras Problem 10.pdf 769.7 kB
12. Quadratic forms and their classification/17.2 Slides_Quadratic surfaces Shortest distance Problem 8.pdf 769.6 kB
7. Inner product as a generalization of dot product/8.1 Slides Inner and outer products.pdf 748.0 kB
7. Inner product as a generalization of dot product/12.2 Slides Quadratic forms and how to read them.pdf 740.7 kB
9. Projections and Gram–Schmidt process in various inner product spaces/13.2 Slides_Gram Schmidt in IP spaces Problem 7.pdf 736.1 kB
4. Intermezzo isomorphic vector spaces/6.1 Slides Why you dont see the difference.pdf 729.3 kB
10. Min-max problems, best approximations, and least squares/3.2 Slides_Min max Problem 2.pdf 718.8 kB
12. Quadratic forms and their classification/18.2 Slides_Quadratic surfaces Problem 9.pdf 714.7 kB
8. Norm, distance, angles, and orthogonality in inner product spaces/18.1 Slides_What is triangle inequality.pdf 706.5 kB
6. Solving systems of linear ODE, and solving higher order ODE/8.2 Slides System of ODE Problem 3.pdf 682.6 kB
8. Norm, distance, angles, and orthogonality in inner product spaces/15.1 Slides_Orthogonality in inner product spaces.pdf 660.8 kB
8. Norm, distance, angles, and orthogonality in inner product spaces/8.1 Slides_First step to defining abstract angles.pdf 655.3 kB
2. Geometrical operators in the plane and in the 3-space/2.1 Slides Eigendecomposition and operators.pdf 654.0 kB
2. Geometrical operators in the plane and in the 3-space/4.1 Notes Problem 2 Projection in the plane.pdf 649.1 kB
2. Geometrical operators in the plane and in the 3-space/3.1 Notes Problem 1 Line symmetry in the plane.pdf 576.8 kB
8. Norm, distance, angles, and orthogonality in inner product spaces/1.2 Slides_Norm in inner product spaces.pdf 575.4 kB
9. Projections and Gram–Schmidt process in various inner product spaces/4.3 Slides_Orthonormal sets of continuous functions Problem 1.pdf 567.8 kB
8. Norm, distance, angles, and orthogonality in inner product spaces/3.2 Slides_Frobenius norm of matrices Problem 1.pdf 559.5 kB
8. Norm, distance, angles, and orthogonality in inner product spaces/2.1 Slides_Weird geometry in the Euclidean space with weighted inner product.pdf 546.3 kB
1. Introduction/1.1 List_of_all_Videos_and_Problems_Linear_Algebra_and_Geometry_3.pdf 541.6 kB
10. Min-max problems, best approximations, and least squares/18.2 Slides_Least squares Problem 11 by projection.pdf 532.7 kB
9. Projections and Gram–Schmidt process in various inner product spaces/6.2 Slides_Orthogonal sets are linearly independent Problem 3.pdf 528.0 kB
4. Intermezzo isomorphic vector spaces/2.1 Slides Different spaces with the same structure.pdf 510.7 kB
7. Inner product as a generalization of dot product/5.2 Slides Inner product spaces.pdf 510.2 kB
10. Min-max problems, best approximations, and least squares/17.2 Slides_Least squares Problem 11 by normal equation.pdf 499.1 kB
7. Inner product as a generalization of dot product/9.2 Slides Weighted Euclidean inner product Problem 1.pdf 479.5 kB
7. Inner product as a generalization of dot product/22.2 Slides Inner product in the space of matrices Problem 6.pdf 469.5 kB
4. Intermezzo isomorphic vector spaces/12.2 Slides Vector spaces Fields Rings Problem 5.pdf 463.8 kB
14. The Grand Finale Singular Value Decomposition and Pseudoinverses/2.1 Slides_Why do we need SVD.pdf 457.6 kB
9. Projections and Gram–Schmidt process in various inner product spaces/9.2 Slides_Projections and orthogonal decomposition in IP spaces Problem 4.pdf 454.1 kB
11. Diagonalization of symmetric matrices/8.2 Slides_The Spectral Theorem Each symmetric matrix is orthogonally diagonalizable.pdf 432.3 kB
5. Recurrence relations, dynamical systems, Markov matrices/9.2 Slides Higher order difference equations Problem 6.pdf 427.3 kB
7. Inner product as a generalization of dot product/7.1 Slides A very important remark about notation.pdf 424.5 kB
8. Norm, distance, angles, and orthogonality in inner product spaces/6.2 Slides_Frobenius distance between matrices Problem 3.pdf 405.1 kB
8. Norm, distance, angles, and orthogonality in inner product spaces/4.2 Slides_Norm in the space of functions Problem 2.pdf 402.4 kB
7. Inner product as a generalization of dot product/4.1 Slides From R^2 to inner product spaces.pdf 399.8 kB
4. Intermezzo isomorphic vector spaces/9.2 Slides Isomorphic spaces Problem 3.pdf 397.1 kB
7. Inner product as a generalization of dot product/18.2 Slides Two inner products in the space of polynomials.pdf 397.1 kB
7. Inner product as a generalization of dot product/16.2 Slides Inner product in the space of continuous functions.pdf 394.9 kB
8. Norm, distance, angles, and orthogonality in inner product spaces/9.2 Slides_Cauchy--Schwarz inequality Proof 1.pdf 393.2 kB
5. Recurrence relations, dynamical systems, Markov matrices/14.2 Slides Markov matrices Problem 9 Migration.pdf 383.2 kB
9. Projections and Gram–Schmidt process in various inner product spaces/10.2 Slides_Projections and orthogonal decomposition in IP spaces Problem 5.pdf 379.5 kB
9. Projections and Gram–Schmidt process in various inner product spaces/14.1 Article-Solved-Problems-Projections-In-Matrix-Spaces.pdf 377.2 kB
10. Min-max problems, best approximations, and least squares/19.2 Slides_Least squares Fitting a line Problem 12.pdf 375.0 kB
12. Quadratic forms and their classification/4.1 Slides_Quadratic forms in two variables Problem 1.pdf 370.4 kB
5. Recurrence relations, dynamical systems, Markov matrices/2.2 Slides Two famous examples of recurrence.pdf 369.5 kB
2. Geometrical operators in the plane and in the 3-space/6.2 Slides Problem 4 Projection in the 3 space.pdf 362.0 kB
7. Inner product as a generalization of dot product/20.1 Slides Inner products in the space of m by n matrices.pdf 358.9 kB
7. Inner product as a generalization of dot product/19.2 Slides The evaluation inner products on P2 Problem 5.pdf 356.6 kB
9. Projections and Gram–Schmidt process in various inner product spaces/2.1 Slides_ON bases in IP spaces.pdf 354.0 kB
9. Projections and Gram–Schmidt process in various inner product spaces/7.1 Slides_Coordinates in orthogonal bases in IP spaces.pdf 353.8 kB
11. Diagonalization of symmetric matrices/4.1 Slides_Complex numbers A brief repetition.pdf 347.7 kB
14. The Grand Finale Singular Value Decomposition and Pseudoinverses/11.2 Slides_Pseudoinverse Problem 3.pdf 346.7 kB
11. Diagonalization of symmetric matrices/12.2 Slides_Orthogonal diagonalization Problem 4.pdf 341.6 kB
10. Min-max problems, best approximations, and least squares/5.2 Slides_Min max Problem 4.pdf 340.8 kB
12. Quadratic forms and their classification/3.1 Slides_What kind of questions we want to answer.pdf 336.0 kB
12. Quadratic forms and their classification/7.1 Slides_Quadratic curves as conic sections.pdf 335.5 kB
2. Geometrical operators in the plane and in the 3-space/5.2 Slides Problem 3 Symmetry in the 3 space.pdf 334.7 kB
12. Quadratic forms and their classification/2.2 Slides_Completing the square is not unique.pdf 334.5 kB
10. Min-max problems, best approximations, and least squares/6.2 Slides_Min max Problem 5.pdf 320.8 kB
10. Min-max problems, best approximations, and least squares/14.1 Slides_Solvability of systems of equations in terms of the column space.pdf 317.9 kB
12. Quadratic forms and their classification/6.1 Slides_Quadratic curves Generally.pdf 317.9 kB
8. Norm, distance, angles, and orthogonality in inner product spaces/5.2 Slides_Distance in inner product spaces.pdf 317.8 kB
5. Recurrence relations, dynamical systems, Markov matrices/13.2 Slides Markov matrices Problem 8 Restaurant.pdf 317.7 kB
10. Min-max problems, best approximations, and least squares/4.2 Slides_Min max Problem 3.pdf 314.5 kB
5. Recurrence relations, dynamical systems, Markov matrices/16.2 Slides Dynamical systems Problem 11.pdf 313.6 kB
2. Geometrical operators in the plane and in the 3-space/7.2 Slides Problem 5 Projection in the 3 space.pdf 313.4 kB
8. Norm, distance, angles, and orthogonality in inner product spaces/12.1 Slides_Angles in inner product spaces.pdf 311.0 kB
5. Recurrence relations, dynamical systems, Markov matrices/10.1 Slides Markov matrices.pdf 310.7 kB
12. Quadratic forms and their classification/12.2 Slides_Classification of curves Problem 5.pdf 307.3 kB
12. Quadratic forms and their classification/11.2 Slides_Classification of curves Problem 4.pdf 303.2 kB
8. Norm, distance, angles, and orthogonality in inner product spaces/17.2 Slides_Orthogonality in inner product spaces Problem 7.pdf 299.5 kB
3. More problem solving; spaces different from R^n/1.2 Slides Eigendecomposition Problem 1.pdf 291.8 kB
7. Inner product as a generalization of dot product/6.2 Slides Euclidean n-space.pdf 285.7 kB
10. Min-max problems, best approximations, and least squares/20.2 Slides_Least squares Fitting a quadratic curve to data Problem 13.pdf 279.6 kB
8. Norm, distance, angles, and orthogonality in inner product spaces/20.2 Slides_Generalized Theorem of Pythagoras.pdf 277.4 kB
4. Intermezzo isomorphic vector spaces/8.2 Slides Isomorphic spaces Problem 2.pdf 265.3 kB
8. Norm, distance, angles, and orthogonality in inner product spaces/21.2 Slides_Generalized Theorem of Pythagoras Problem 8.pdf 251.8 kB
5. Recurrence relations, dynamical systems, Markov matrices/7.2 Slides Higher order difference equations Problem 4.pdf 247.6 kB
4. Intermezzo isomorphic vector spaces/3.1 Slides More examples of isomorphic vector spaces.pdf 246.3 kB
11. Diagonalization of symmetric matrices/14.2 Slides_Orthogonal diagonalization Problem 6.pdf 245.1 kB
11. Diagonalization of symmetric matrices/15.2 Slides_Orthogonal diagonalization Problem 7.pdf 243.3 kB
5. Recurrence relations, dynamical systems, Markov matrices/3.1 Slides Linear discrete dynamical systems.pdf 236.5 kB
3. More problem solving; spaces different from R^n/4.2 Slides Powers and roots Problem 4.pdf 233.9 kB
5. Recurrence relations, dynamical systems, Markov matrices/5.2 Slides Systems of difference equations Problem 2.pdf 226.4 kB
8. Norm, distance, angles, and orthogonality in inner product spaces/10.2 Slides_Cauchy--Schwarz inequality Proof 2.pdf 220.0 kB
11. Diagonalization of symmetric matrices/13.2 Slides_Orthogonal diagonalization Problem 5.pdf 215.4 kB
3. More problem solving; spaces different from R^n/2.2 Slides Eigendecomposition Problem 2.pdf 210.4 kB
3. More problem solving; spaces different from R^n/7.2 Slides In the space of matrices Problem 7.pdf 207.6 kB
11. Diagonalization of symmetric matrices/9.1 Slides_Orthogonal diagonalization How to do it.pdf 205.8 kB
5. Recurrence relations, dynamical systems, Markov matrices/1.1 Slides Continuous versus discrete.pdf 197.7 kB
5. Recurrence relations, dynamical systems, Markov matrices/6.2 Slides Systems of difference equations Problem 3.pdf 195.9 kB
5. Recurrence relations, dynamical systems, Markov matrices/8.2 Slides Higher order difference equations Problem 5.pdf 188.9 kB
10. Min-max problems, best approximations, and least squares/15.1 Slides_Least squares solution and residual vector.pdf 171.7 kB
10. Min-max problems, best approximations, and least squares/10.2 Slides_Shortest distance from a subspace.pdf 160.6 kB
5. Recurrence relations, dynamical systems, Markov matrices/15.2 Slides Markov matrices Problem 10 Election.pdf 160.6 kB
11. Diagonalization of symmetric matrices/8.1 Article-Spectral-Theorem-Proof-of-Lemma-2.pdf 152.7 kB
5. Recurrence relations, dynamical systems, Markov matrices/11.1 Slides Each Markov matrix has eigenvalue one.pdf 148.1 kB
9. Projections and Gram–Schmidt process in various inner product spaces/4.1 Article-Riemann-integrals-repetition-trig-integrals.pdf 146.6 kB
8. Norm, distance, angles, and orthogonality in inner product spaces/11.1 Slides_Cauchy--Schwarz inequality in the space of continuous functions.pdf 146.2 kB
11. Diagonalization of symmetric matrices/17.1 Article-Solved-Problems-Positive-Negative-Definite-Completing-the-Square.pdf 127.9 kB
7. Inner product as a generalization of dot product/1.1 Slides Between concrete and abstract.pdf 126.5 kB
9. Projections and Gram–Schmidt process in various inner product spaces/3.2 Slides_Why does normalizing work in the same way in all IP spaces.pdf 121.5 kB
14. The Grand Finale Singular Value Decomposition and Pseudoinverses/4.1 Article-SVD-theory.pdf 116.4 kB
11. Diagonalization of symmetric matrices/2.1 Slides_Some properties of symmetric matrices.pdf 102.5 kB

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