1 | 1. Introduction to the Course Contents. | PDF unavailable |
2 | 2. Linear Equations | PDF unavailable |
3 | 3a. Equivalent Systems of Linear Equations I: Inverses of Elementary Row-operations, Row-equivalent matrices | PDF unavailable |
4 | 3b. Equivalent Systems of Linear Equations II: Homogeneous Equations, Examples | PDF unavailable |
5 | 4. Row-reduced Echelon Matrices | PDF unavailable |
6 | 5. Row-reduced Echelon Matrices and Non-homogeneous Equations | PDF unavailable |
7 | 6. Elementary Matrices, Homogeneous Equations and Non-homogeneous Equations | PDF unavailable |
8 | 7. Invertible matrices, Homogeneous Equations Non-homogeneous Equations | PDF unavailable |
9 | 8. Vector spaces | PDF unavailable |
10 | 9. Elementary Properties in Vector Spaces. Subspaces | PDF unavailable |
11 | 10. Subspaces (continued), Spanning Sets, Linear Independence, Dependence | PDF unavailable |
12 | 11. Basis for a vector space | PDF unavailable |
13 | 12. Dimension of a vector space | PDF unavailable |
14 | 13. Dimensions of Sums of Subspaces | PDF unavailable |
15 | 14. Linear Transformations | PDF unavailable |
16 | 15. The Null Space and the Range Space of a Linear Transformation | PDF unavailable |
17 | 16. The Rank-Nullity-Dimension Theorem. Isomorphisms Between Vector Spaces | PDF unavailable |
18 | 17. Isomorphic Vector Spaces, Equality of the Row-rank and the Column-rank I | PDF unavailable |
19 | 18. Equality of the Row-rank and the Column-rank II | PDF unavailable |
20 | 19. The Matrix of a Linear Transformation | PDF unavailable |
21 | 20. Matrix for the Composition and the Inverse. Similarity Transformation | PDF unavailable |
22 | 21. Linear Functionals. The Dual Space. Dual Basis I | PDF unavailable |
23 | 22. Dual Basis II. Subspace Annihilators I | PDF unavailable |
24 | 23. Subspace Annihilators II | PDF unavailable |
25 | 24. The Double Dual. The Double Annihilator | PDF unavailable |
26 | 25. The Transpose of a Linear Transformation. Matrices of a Linear Transformation and its Transpose | PDF unavailable |
27 | 26. Eigenvalues and Eigenvectors of Linear Operators | PDF unavailable |
28 | 27. Diagonalization of Linear Operators. A Characterization | PDF unavailable |
29 | 28. The Minimal Polynomial | PDF unavailable |
30 | 29. The Cayley-Hamilton Theorem | PDF unavailable |
31 | 30. Invariant Subspaces | PDF unavailable |
32 | 31. Triangulability, Diagonalization in Terms of the Minimal Polynomial | PDF unavailable |
33 | 32. Independent Subspaces and Projection Operators | PDF unavailable |
34 | 33. Direct Sum Decompositions and Projection Operators I | PDF unavailable |
35 | 34. Direct Sum Decomposition and Projection Operators II | PDF unavailable |
36 | 35. The Primary Decomposition Theorem and Jordan Decomposition | PDF unavailable |
37 | 36. Cyclic Subspaces and Annihilators | PDF unavailable |
38 | 37. The Cyclic Decomposition Theorem I | PDF unavailable |
39 | 38. The Cyclic Decomposition Theorem II. The Rational Form | PDF unavailable |
40 | 39. Inner Product Spaces | PDF unavailable |
41 | 40. Norms on Vector spaces. The Gram-Schmidt Procedure I | PDF unavailable |
42 | 41. The Gram-Schmidt Procedure II. The QR Decomposition. | PDF unavailable |
43 | 42. Bessel's Inequality, Parseval's Indentity, Best Approximation | PDF unavailable |
44 | 43. Best Approximation: Least Squares Solutions | PDF unavailable |
45 | 44. Orthogonal Complementary Subspaces, Orthogonal Projections | PDF unavailable |
46 | 45. Projection Theorem. Linear Functionals | PDF unavailable |
47 | 46. The Adjoint Operator | PDF unavailable |
48 | 47. Properties of the Adjoint Operation. Inner Product Space Isomorphism | PDF unavailable |
49 | 48. Unitary Operators | PDF unavailable |
50 | 49. Unitary operators II. Self-Adjoint Operators I. | PDF unavailable |
51 | 50. Self-Adjoint Operators II - Spectral Theorem | PDF unavailable |
52 | 51. Normal Operators - Spectral Theorem | PDF unavailable |