Linear Algebra Video Lectures

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