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9. Independence, Basis, and Dimension

18.06 - Linear Algebra

其他影片 (36)

1 An Interview with Gilbert Strang on Teaching Linear Algebra 2 1. The Geometry of Linear Equations 3 2. Elimination with Matrices. 4 3. Multiplication and Inverse Matrices 5 4. Factorization into A = LU 6 5. Transposes, Permutations, Spaces R^n 7 6. Column Space and Nullspace 8 7. Solving Ax = 0: Pivot Variables, Special Solutions 9 8. Solving Ax = b: Row Reduced Form R 10 9. Independence, Basis, and Dimension 11 10. The Four Fundamental Subspaces 12 11. Matrix Spaces; Rank 1; Small World Graphs 13 12. Graphs, Networks, Incidence Matrices 14 13. Quiz 1 Review 15 14. Orthogonal Vectors and Subspaces 16 15. Projections onto Subspaces 17 16. Projection Matrices and Least Squares 18 17. Orthogonal Matrices and Gram-Schmidt 19 18. Properties of Determinants 20 19. Determinant Formulas and Cofactors 21 20. Cramer's Rule, Inverse Matrix, and Volume 22 21. Eigenvalues and Eigenvectors 23 22. Diagonalization and Powers of A 24 23. Differential Equations and exp(At) 25 24. Markov Matrices; Fourier Series 26 24b. Quiz 2 Review 27 25. Symmetric Matrices and Positive Definiteness 28 26. Complex Matrices; Fast Fourier Transform 29 27. Positive Definite Matrices and Minima 30 28. Similar Matrices and Jordan Form 31 29. Singular Value Decomposition 32 30. Linear Transformations and Their Matrices 33 31. Change of Basis; Image Compression 34 32. Quiz 3 Review 35 33. Left and Right Inverses; Pseudoinverse 36 34. Final Course Review

AI 學習助教

Linear Algebra

課程影片 (36)

1 An Interview with Gilbert Strang on Teaching Linear Algebra 2 1. The Geometry of Linear Equations 3 2. Elimination with Matrices. 4 3. Multiplication and Inverse Matrices 5 4. Factorization into A = LU 6 5. Transposes, Permutations, Spaces R^n 7 6. Column Space and Nullspace 8 7. Solving Ax = 0: Pivot Variables, Special Solutions 9 8. Solving Ax = b: Row Reduced Form R 10 9. Independence, Basis, and Dimension 11 10. The Four Fundamental Subspaces 12 11. Matrix Spaces; Rank 1; Small World Graphs 13 12. Graphs, Networks, Incidence Matrices 14 13. Quiz 1 Review 15 14. Orthogonal Vectors and Subspaces 16 15. Projections onto Subspaces 17 16. Projection Matrices and Least Squares 18 17. Orthogonal Matrices and Gram-Schmidt 19 18. Properties of Determinants 20 19. Determinant Formulas and Cofactors 21 20. Cramer's Rule, Inverse Matrix, and Volume 22 21. Eigenvalues and Eigenvectors 23 22. Diagonalization and Powers of A 24 23. Differential Equations and exp(At) 25 24. Markov Matrices; Fourier Series 26 24b. Quiz 2 Review 27 25. Symmetric Matrices and Positive Definiteness 28 26. Complex Matrices; Fast Fourier Transform 29 27. Positive Definite Matrices and Minima 30 28. Similar Matrices and Jordan Form 31 29. Singular Value Decomposition 32 30. Linear Transformations and Their Matrices 33 31. Change of Basis; Image Compression 34 32. Quiz 3 Review 35 33. Left and Right Inverses; Pseudoinverse 36 34. Final Course Review