Topics in this module:
1. First Basic Problem – Systems of Linear equations - Matrix Notation – The various questions that arise with a system of linear equations
2. Second Basic Problem – Diagonalization of a square matrix – The various questions that arise with diagonalization

1. Systems of Linear Equations
2. Matrix Notation
3. Diagonalization of a Square Matrix
4. Linear Systems Part 1
5. Linear Systems Part 2
6. Linear Systems Part 3
7. Linear Systems Part 4
8. Vector Spaces Part 1
9. Vector Spaces Part 2
10. Linear Independence and Subspaces Part 1
11. Linear Independence and Subspaces Part 2
12. Linear Independence and Subspaces Part 3
13. Linear Independence and Subspaces Part 4
14. Basis Part 1
15. Basis Part 2
16. Basis Part 3
17. Linear Transformations Part 1
18. Linear Transformations Part 2
19. Linear Transformations Part 3
20. Linear Transformations Part 4
21. Linear Transformations Part 5
22. Inner Product and Orthogonality Part 1
23. Inner Product and Orthogonality Part 2
24. Inner Product and Orthogonality Part 3
25. Inner Product and Orthogonality Part 4
26. Inner Product and Orthogonality Part 5
27. Inner Product and Orthogonality Part 6
28. Diagonalization Part 1
29. Diagonalization Part 2
30. Diagonalization Part 3
31. Diagonalization Part 4
32. Hermitian and Symmetric matrices Part 1
33. Hermitian and Symmetric matrices Part 2
34. Hermitian and Symmetric matrices Part 3
35. Hermitian and Symmetric matrices Part 4
36. Singular Value Decomposition (SVD) Part 1
37. Singular Value Decomposition (SVD) Part 2
38. Back To Linear Systems Part 1
39. Back To Linear Systems Part 2
40. Epilogue

This is Advanced Matrix Theory and Linear Algebra for Engineers by Prof. Vittal Rao ,Centre For Electronics Design and Technology, IISC Bangalore. Topics include Introduction, Vector Spaces, Solutions of Linear Systems, Important Subspaces associated with a matrix, Orthogonality, Eigenvalues and Eigenvectors, Diagonalizable Matrices, Hermitian Matrices, General Matrices, Jordan Canonical form (Optional)*, Selected Topics in Applications (Optional).