# Matrix Theory and Applications

- Institution: IIT Hyderabad
- Department: Electrical Engineering
- Teacher: Prof. Aditya Siripuram
- Level: Undergraduate
- Language: English
- Subjects: Engineering
- Source: [NPTEL](https://nptel.ac.in/courses/108106002)
- Licence: [CC BY-NC-SA](https://nptel.ac.in/faq) (Non-commercial use only.)
- Syllabus: [at the source](https://nptel.ac.in/courses/108106002)
- Who can watch: Tweens profiles and older (sources give no ratings; placed by Invisible Network from the source's own words)

## Lectures

1. [Vectors: definitions and operations](https://invisiblenetwork.ai/learn/nptel/108106002/cc85fff63885) (YouTube)
2. [Inner products and linear functions](https://invisiblenetwork.ai/learn/nptel/108106002/e41d0082ca2f) (YouTube)
3. [Norms, distances, and the Cauchy–Schwarz inequality](https://invisiblenetwork.ai/learn/nptel/108106002/805043d38f95) (YouTube)
4. [Projection onto a vector](https://invisiblenetwork.ai/learn/nptel/108106002/d18342d64acc) (YouTube)
5. [Vector spaces and general inner products](https://invisiblenetwork.ai/learn/nptel/108106002/914dbac123bd) (YouTube)
6. [Norms beyond Euclidean](https://invisiblenetwork.ai/learn/nptel/108106002/0f9c66cb5c92) (YouTube)
7. [Complexity of vector operations](https://invisiblenetwork.ai/learn/nptel/108106002/fef0c64b6d61) (YouTube)
8. [Matrices and their action](https://invisiblenetwork.ai/learn/nptel/108106002/f8fbc632e220) (YouTube)
9. [Matrix products and transpose](https://invisiblenetwork.ai/learn/nptel/108106002/1f4b42241aa0) (YouTube)
10. [More on the transpose](https://invisiblenetwork.ai/learn/nptel/108106002/9333e5283055) (YouTube)
11. [A battery of examples: structural matrix families](https://invisiblenetwork.ai/learn/nptel/108106002/7a189b9e994d) (YouTube)
12. [A battery of examples: matrices from applications](https://invisiblenetwork.ai/learn/nptel/108106002/4bddec0cc64b) (YouTube)
13. [Block matrices, linear maps, and the Jacobian](https://invisiblenetwork.ai/learn/nptel/108106002/fd66fa7c6fd9) (YouTube)
14. [Systems and examples](https://invisiblenetwork.ai/learn/nptel/108106002/ade8e4d00d78) (YouTube)
15. [Existence and structure](https://invisiblenetwork.ai/learn/nptel/108106002/dfc3c8b3ff9e) (YouTube)
16. [Example systems, stability](https://invisiblenetwork.ai/learn/nptel/108106002/063982cebd0a) (YouTube)
17. [Matrix maps: injectivity, surjectivity, inverses](https://invisiblenetwork.ai/learn/nptel/108106002/92f2a64a05fe) (YouTube)
18. [Null space and linear independence](https://invisiblenetwork.ai/learn/nptel/108106002/b9e996a038cb) (YouTube)
19. [Subspaces and the image space](https://invisiblenetwork.ai/learn/nptel/108106002/18731e446ce6) (YouTube)
20. [Easy facts about linear independence](https://invisiblenetwork.ai/learn/nptel/108106002/166705348106) (YouTube)
21. [Growing linearly independent sets](https://invisiblenetwork.ai/learn/nptel/108106002/68dff1a39f3f) (YouTube)
22. [Dimension and basis](https://invisiblenetwork.ai/learn/nptel/108106002/66e2aa66005f) (YouTube)
23. [Rank and nullity Part_1](https://invisiblenetwork.ai/learn/nptel/108106002/6e6edbeb5f7c) (YouTube)
24. [Rank and nullity Part _2](https://invisiblenetwork.ai/learn/nptel/108106002/60471a77aec6) (YouTube)
25. [The rank–nullity theorem](https://invisiblenetwork.ai/learn/nptel/108106002/d40b227cea9c) (YouTube)
26. [Rank, the transpose, and the inverse](https://invisiblenetwork.ai/learn/nptel/108106002/0c589f5fefe8) (YouTube)
27. [Examples: rank and nullity at work](https://invisiblenetwork.ai/learn/nptel/108106002/1a3d7a184441) (YouTube)
28. [Orthogonal complements](https://invisiblenetwork.ai/learn/nptel/108106002/21cde6bf5a3f) (YouTube)
29. [Orthonormal bases and the residual](https://invisiblenetwork.ai/learn/nptel/108106002/4d675d2e54a7) (YouTube)
30. [Gram–Schmidt and the QR decomposition](https://invisiblenetwork.ai/learn/nptel/108106002/7e24f6e70f52) (YouTube)
31. [Solving systems and finding bases with QR](https://invisiblenetwork.ai/learn/nptel/108106002/966fe4799500) (YouTube)
32. [Projections and least squares](https://invisiblenetwork.ai/learn/nptel/108106002/b5ffba56e0d3) (YouTube)
33. [Cost, and the trouble with Gram–Schmidt](https://invisiblenetwork.ai/learn/nptel/108106002/aba5d68cb302) (YouTube)
34. [Recap: least squares](https://invisiblenetwork.ai/learn/nptel/108106002/ecf6f7915f49) (YouTube)
35. [Projections in general](https://invisiblenetwork.ai/learn/nptel/108106002/98e6f35cba92) (YouTube)
36. [Least squares with constraints](https://invisiblenetwork.ai/learn/nptel/108106002/4043016a3179) (YouTube)
37. [solving constrained least squares](https://invisiblenetwork.ai/learn/nptel/108106002/b23d3231887b) (YouTube)
38. [Regularization and gradient descent](https://invisiblenetwork.ai/learn/nptel/108106002/a5118a961ea1) (YouTube)
39. [Optional - Solving augumented System](https://invisiblenetwork.ai/learn/nptel/108106002/2c2f3f75bdd4) (YouTube)
40. [Recursive Least squares - part1](https://invisiblenetwork.ai/learn/nptel/108106002/3067d4e4ae0b) (YouTube)
41. [Recursive Least squares - part2](https://invisiblenetwork.ai/learn/nptel/108106002/c15e08df8db7) (YouTube)
42. [Multi Objective Least squares](https://invisiblenetwork.ai/learn/nptel/108106002/b1676953349e) (YouTube)
43. [Non linear Least squares](https://invisiblenetwork.ai/learn/nptel/108106002/c063ebb30526) (YouTube)
44. [Matrix Least squares](https://invisiblenetwork.ai/learn/nptel/108106002/41abd21a8ace) (YouTube)
45. [(Optional) Estimation:Random variables as vectors](https://invisiblenetwork.ai/learn/nptel/108106002/966cb3a4f1c3) (YouTube)
46. [Dimensionality Reduction and graph drawing](https://invisiblenetwork.ai/learn/nptel/108106002/e1b5069b3db1) (YouTube)
47. [Repeated matrix action and quadratic forms](https://invisiblenetwork.ai/learn/nptel/108106002/37912927fd8f) (YouTube)
48. [Eigenvectors and eigenvalues](https://invisiblenetwork.ai/learn/nptel/108106002/b23668bf7996) (YouTube)
49. [Diagonalizability](https://invisiblenetwork.ai/learn/nptel/108106002/228a14fb63b3) (YouTube)
50. [The spectral theorem and rayleigh quotient](https://invisiblenetwork.ai/learn/nptel/108106002/5d030cfc7716) (YouTube)
51. [Dimensionality Reduction and graph drawing in one dimension](https://invisiblenetwork.ai/learn/nptel/108106002/b4c5631e1498) (YouTube)
52. [Recurrences through the eigenbasis](https://invisiblenetwork.ai/learn/nptel/108106002/412927a9fa23) (YouTube)
53. [The power method and the disc theorem](https://invisiblenetwork.ai/learn/nptel/108106002/090b5a82f4fa) (YouTube)
54. [Powers of stochastic Matrix - Part 1](https://invisiblenetwork.ai/learn/nptel/108106002/dc5da3ca46bc) (YouTube)
55. [Powers of stochastic Matrix - Part 2](https://invisiblenetwork.ai/learn/nptel/108106002/0a1e50895869) (YouTube)
56. [Gradient descent on Least squares - Part 1](https://invisiblenetwork.ai/learn/nptel/108106002/09865a9ee567) (YouTube)
57. [Gradient descent on Least squares - Part 2](https://invisiblenetwork.ai/learn/nptel/108106002/75c8befc52b5) (YouTube)
58. [The Trace](https://invisiblenetwork.ai/learn/nptel/108106002/9731d7ee48cb) (YouTube)
59. [Ky fan's theorem : maximizing over k directions](https://invisiblenetwork.ai/learn/nptel/108106002/fea8d9305e12) (YouTube)
60. [Dimensionally reduction abd graph drawing in two dimensions](https://invisiblenetwork.ai/learn/nptel/108106002/50d4efca5e4e) (YouTube)
61. [Determinants and the characteristic polynomial](https://invisiblenetwork.ai/learn/nptel/108106002/d7e45b1eaab7) (YouTube)
62. [Optional: Proof of the spectral theorem - Part 1](https://invisiblenetwork.ai/learn/nptel/108106002/a16f69514106) (YouTube)
63. [Optional: Proof of the spectral theorem - Part 2](https://invisiblenetwork.ai/learn/nptel/108106002/c68897a56714) (YouTube)
64. [Singular values via low rank approximation - Part 1](https://invisiblenetwork.ai/learn/nptel/108106002/0115142016aa) (YouTube)
65. [Singular values via low rank approximation - Part 2](https://invisiblenetwork.ai/learn/nptel/108106002/8880a8e6c5b8) (YouTube)
66. [Singular values via low rank approximation - Part 3](https://invisiblenetwork.ai/learn/nptel/108106002/942f6511b9c8) (YouTube)
67. [The singular value decomposition - Part 1](https://invisiblenetwork.ai/learn/nptel/108106002/38f85a858b33) (YouTube)
68. [The singular value decomposition - Part 2](https://invisiblenetwork.ai/learn/nptel/108106002/b46aebf4a224) (YouTube)
69. [The pseudo inverse](https://invisiblenetwork.ai/learn/nptel/108106002/ba1c8fab83d4) (YouTube)
70. [Spectral norm and condition number](https://invisiblenetwork.ai/learn/nptel/108106002/fccc7022a2fc) (YouTube)
71. [Orthogonal Procustes](https://invisiblenetwork.ai/learn/nptel/108106002/fad6357f5c29) (YouTube)
72. [Low rank approximation](https://invisiblenetwork.ai/learn/nptel/108106002/b299cac8ac8f) (YouTube)
73. [Sketching for least squares - Part 1](https://invisiblenetwork.ai/learn/nptel/108106002/90ae6837cac9) (YouTube)
74. [Sketching for least squares - Part 2](https://invisiblenetwork.ai/learn/nptel/108106002/140045b0a95a) (YouTube)
75. [Sketching for least squares - Part 3](https://invisiblenetwork.ai/learn/nptel/108106002/ae613abafc49) (YouTube)
76. [Kaczmarz's method and stochastic gradient descent for least squares](https://invisiblenetwork.ai/learn/nptel/108106002/4d94f4812c22) (YouTube)