# Matrix Theory

- Institution: IISc Bangalore
- Department: Mathematics
- Teacher: Prof. Chandra Murthy
- Level: Undergraduate
- Language: English
- Subjects: Mathematics
- Source: [NPTEL](https://nptel.ac.in/courses/111108157)
- Licence: [CC BY-NC-SA](https://nptel.ac.in/faq) (Non-commercial use only.)
- Syllabus: [at the source](https://nptel.ac.in/courses/111108157)
- Who can watch: Tweens profiles and older (sources give no ratings; placed by Invisible Network from the source's own words)

## Lectures

1. [Course introduction and properties of matrices](https://invisiblenetwork.ai/learn/nptel/111108157/cbc937e47a3c) (Video)
2. [Vector spaces](https://invisiblenetwork.ai/learn/nptel/111108157/8debe5960aaa) (Video)
3. [Basis, dimension](https://invisiblenetwork.ai/learn/nptel/111108157/c833105ce5d6) (Video)
4. [Linear transforms](https://invisiblenetwork.ai/learn/nptel/111108157/da7880d6de68) (Video)
5. [Fundamental subspaces of a matrix](https://invisiblenetwork.ai/learn/nptel/111108157/f52b1f110c66) (Video)
6. [Fundamental theorem of linear algebra](https://invisiblenetwork.ai/learn/nptel/111108157/0a71a69adc6e) (Video)
7. [Properties of rank](https://invisiblenetwork.ai/learn/nptel/111108157/be37ea4bf38d) (Video)
8. [Inner product](https://invisiblenetwork.ai/learn/nptel/111108157/fe1d734ce003) (Video)
9. [Gram-schmidt algorithm](https://invisiblenetwork.ai/learn/nptel/111108157/06768ad3a3a7) (Video)
10. [Orthonormal matrices definition](https://invisiblenetwork.ai/learn/nptel/111108157/9e547822be98) (Video)
11. [Determinant](https://invisiblenetwork.ai/learn/nptel/111108157/e16e5e578bcb) (Video)
12. [Properties of determinants](https://invisiblenetwork.ai/learn/nptel/111108157/d064a5967664) (Video)
13. [Introduction to norms and inner products](https://invisiblenetwork.ai/learn/nptel/111108157/a6d262b765aa) (Video)
14. [Vector norms and their properties,](https://invisiblenetwork.ai/learn/nptel/111108157/9e775e0c44fa) (Video)
15. [Applications and equivalence of vector norms](https://invisiblenetwork.ai/learn/nptel/111108157/a18d38e8f959) (Video)
16. [Summary of equivalence of norms](https://invisiblenetwork.ai/learn/nptel/111108157/cb7707f7fcdb) (Video)
17. [Dual norms](https://invisiblenetwork.ai/learn/nptel/111108157/aa0d2514bf09) (Video)
18. [Properties and examples of dual norms](https://invisiblenetwork.ai/learn/nptel/111108157/4ff62cfe9add) (Video)
19. [Matrix norms](https://invisiblenetwork.ai/learn/nptel/111108157/23405bf2dc7b) (Video)
20. [Matrix norms: Properties](https://invisiblenetwork.ai/learn/nptel/111108157/435570630668) (Video)
21. [Induced norms](https://invisiblenetwork.ai/learn/nptel/111108157/20905be63fb7) (Video)
22. [Induced norms and examples](https://invisiblenetwork.ai/learn/nptel/111108157/a19dc67d3f22) (Video)
23. [Spectral radius](https://invisiblenetwork.ai/learn/nptel/111108157/e0fce7b954a2) (Video)
24. [Properties of spectral radius](https://invisiblenetwork.ai/learn/nptel/111108157/81a5b30b2dff) (Video)
25. [Convergent matrices, Banach lemma](https://invisiblenetwork.ai/learn/nptel/111108157/1dbc343c5704) (Video)
26. [Recap of matrix norms and Levy-Desplanques theorem](https://invisiblenetwork.ai/learn/nptel/111108157/8eb2d273b541) (Video)
27. [Equivalence of matrix norms and error in inverses of linear systems](https://invisiblenetwork.ai/learn/nptel/111108157/54f3ddf9c2d3) (Video)
28. [Errors in inverses of matrices](https://invisiblenetwork.ai/learn/nptel/111108157/fbd35506e053) (Video)
29. [Errors in solving systems of linear equations](https://invisiblenetwork.ai/learn/nptel/111108157/71bdcce4e5f2) (Video)
30. [Introduction to eigenvalues and eigenvectors](https://invisiblenetwork.ai/learn/nptel/111108157/e389f60f5eda) (Video)
31. [The characteristic polynomial](https://invisiblenetwork.ai/learn/nptel/111108157/71e9b1058b5e) (Video)
32. [Solving characteristic polynomials, eigenvectors properties](https://invisiblenetwork.ai/learn/nptel/111108157/dfaefebe27a7) (Video)
33. [Similarity](https://invisiblenetwork.ai/learn/nptel/111108157/d30340b23110) (Video)
34. [Diagonalization](https://invisiblenetwork.ai/learn/nptel/111108157/94c6854fa5ed) (Video)
35. [Relationship between eigenvalues of BA and AB](https://invisiblenetwork.ai/learn/nptel/111108157/21f827d0a38a) (Video)
36. [Eigenvector and principle of biorthogonality](https://invisiblenetwork.ai/learn/nptel/111108157/bcf278d86453) (Video)
37. [Unitary matrices](https://invisiblenetwork.ai/learn/nptel/111108157/d491a9adfb88) (Video)
38. [Properties of unitary matrices](https://invisiblenetwork.ai/learn/nptel/111108157/2497ed2fc98b) (Video)
39. [Unitary equivalence](https://invisiblenetwork.ai/learn/nptel/111108157/d0b19cae9e54) (Video)
40. [Schur's triangularization theorem](https://invisiblenetwork.ai/learn/nptel/111108157/19a2fcc78a8c) (Video)
41. [Cayley-Hamilton theorem](https://invisiblenetwork.ai/learn/nptel/111108157/e44e72f8f531) (Video)
42. [Uses of cayley-hamilton theorem and diagonalizability revisited](https://invisiblenetwork.ai/learn/nptel/111108157/12b04d9970c9) (Video)
43. [Normal matrices: Definition and fundamental properties](https://invisiblenetwork.ai/learn/nptel/111108157/9878d81c714b) (Video)
44. [Fundamental properties of normal matrices](https://invisiblenetwork.ai/learn/nptel/111108157/257f6942548e) (Video)
45. [QR decomposition and canonical forms](https://invisiblenetwork.ai/learn/nptel/111108157/f8a1f33d6d3c) (Video)
46. [Jordan canonical form](https://invisiblenetwork.ai/learn/nptel/111108157/5b901f8cd331) (Video)
47. [Determining the Jordan form of a matrix](https://invisiblenetwork.ai/learn/nptel/111108157/42295fa0cb85) (Video)
48. [Properties of the Jordan canonical form (part 1)](https://invisiblenetwork.ai/learn/nptel/111108157/9d0f16a73257) (Video)
49. [Properties of the Jordan canonical form (part 2)](https://invisiblenetwork.ai/learn/nptel/111108157/ce9b46d7b4fc) (Video)
50. [Properties of convergent matrices](https://invisiblenetwork.ai/learn/nptel/111108157/a12713bfc0b0) (Video)
51. [Polynomials and matrices](https://invisiblenetwork.ai/learn/nptel/111108157/b1814363ef37) (Video)
52. [Other canonical forms and factorization of matrices: Gaussian elimination & LU factorization](https://invisiblenetwork.ai/learn/nptel/111108157/aac44209a20a) (Video)
53. [LU decomposition](https://invisiblenetwork.ai/learn/nptel/111108157/2d9d03e75f92) (Video)
54. [LU decomposition with pivoting](https://invisiblenetwork.ai/learn/nptel/111108157/3fd1b91a9102) (Video)
55. [Solving pivoted system and LDM decomposition](https://invisiblenetwork.ai/learn/nptel/111108157/242a1070e11c) (Video)
56. [Cholesky decomposition and uses](https://invisiblenetwork.ai/learn/nptel/111108157/7c149a9664d4) (Video)
57. [Hermitian and symmetric matrix](https://invisiblenetwork.ai/learn/nptel/111108157/c3fa828bb311) (Video)
58. [Properties of hermitian matrices](https://invisiblenetwork.ai/learn/nptel/111108157/8ada6546f724) (Video)
59. [Variational characterization of Eigenvalues: Rayleigh-Ritz theorem](https://invisiblenetwork.ai/learn/nptel/111108157/d6cf2c188c7f) (Video)
60. [Variational characterization of eigenvalues (continued)](https://invisiblenetwork.ai/learn/nptel/111108157/c24dcac011ad) (Video)
61. [Courant-Fischer theorem](https://invisiblenetwork.ai/learn/nptel/111108157/18b9c1f841d9) (Video)
62. [Summary of Rayliegh-Ritz and Courant-Fischer theorems](https://invisiblenetwork.ai/learn/nptel/111108157/0c82adcb9ba6) (Video)
63. [Weyl's theorem](https://invisiblenetwork.ai/learn/nptel/111108157/1a84b0777155) (Video)
64. [Positive semi-definite matrix, monotonicity theorem and interlacing theorems](https://invisiblenetwork.ai/learn/nptel/111108157/d33974df74c3) (Video)
65. [Interlacing theorem I](https://invisiblenetwork.ai/learn/nptel/111108157/96ddb2723053) (Video)
66. [Interlacing theorem II (Converse)](https://invisiblenetwork.ai/learn/nptel/111108157/1b8dcd3254c2) (Video)
67. [Interlacing theorem (Continued)](https://invisiblenetwork.ai/learn/nptel/111108157/70137454d281) (Video)
68. [Eigenvalues: Majorization theorem and proof](https://invisiblenetwork.ai/learn/nptel/111108157/f4b5f7c75809) (Video)
69. [Location and perturbation of Eigenvalues Part1: Dominant diagonal theorem](https://invisiblenetwork.ai/learn/nptel/111108157/9b17495e1d05) (Video)
70. [Location and perturbation of Eigenvalues Part2: Gersgorin's theorem](https://invisiblenetwork.ai/learn/nptel/111108157/c967052359ae) (Video)
71. [Implications of Gersgorin disc theorem, condition of eigenvalues](https://invisiblenetwork.ai/learn/nptel/111108157/dc33b0d41e3f) (Video)
72. [Condition of eigenvalues for diagonalizable matrices](https://invisiblenetwork.ai/learn/nptel/111108157/20bc353d73eb) (Video)
73. [Perturbation of eigenvalues Birkhoff's theorem Hoffman - Weilandt theorem](https://invisiblenetwork.ai/learn/nptel/111108157/75d9f05324e6) (Video)
74. [Singular value definition and some remarks.](https://invisiblenetwork.ai/learn/nptel/111108157/3a941e217208) (Video)
75. [Proof of singular value decomposition theorem.](https://invisiblenetwork.ai/learn/nptel/111108157/31f4d4a521cc) (Video)
76. [Partitioning the SVD](https://invisiblenetwork.ai/learn/nptel/111108157/3233cc755fd1) (Video)
77. [Properties of SVD](https://invisiblenetwork.ai/learn/nptel/111108157/c47e82ab25e1) (Video)
78. [Generalized inverse of matrices](https://invisiblenetwork.ai/learn/nptel/111108157/e78a37e32db2) (Video)
79. [Least squares](https://invisiblenetwork.ai/learn/nptel/111108157/108405ed80b7) (Video)
80. [Constrained least squares](https://invisiblenetwork.ai/learn/nptel/111108157/0ce6df10e107) (Video)