# Applied Linear Algebra

- Institution: IIT Bombay
- Department: Electrical Engineering
- Teacher: Prof. Dwaipayan Mukherjee
- Level: Undergraduate
- Language: English
- Subjects: Engineering
- Source: [NPTEL](https://nptel.ac.in/courses/108101371)
- Licence: [CC BY-NC-SA](https://nptel.ac.in/faq) (Non-commercial use only.)
- Syllabus: [at the source](https://nptel.ac.in/courses/108101371)
- Who can watch: Tweens profiles and older (sources give no ratings; placed by Invisible Network from the source's own words)

## Lectures

1. [Lecture 1 - Introduction - Part A](https://invisiblenetwork.ai/learn/nptel/108101371/8ad4067b83ea) (Video)
2. [Lecture 2 - Introduction - Part B](https://invisiblenetwork.ai/learn/nptel/108101371/e52231da7ddc) (Video)
3. [Lecture 3 - Introduction - Part C](https://invisiblenetwork.ai/learn/nptel/108101371/064a354408a7) (Video)
4. [Lecture 4 - Equivalent Systems - Part A](https://invisiblenetwork.ai/learn/nptel/108101371/b378f59b93e1) (Video)
5. [Lecture 5 - Equivalent Systems - Part B](https://invisiblenetwork.ai/learn/nptel/108101371/961842f9e519) (Video)
6. [Lecture 6 - Equivalent Systems - Part C](https://invisiblenetwork.ai/learn/nptel/108101371/089c9d6672cf) (Video)
7. [Lecture 7 - Solution of Ax = b - Part A](https://invisiblenetwork.ai/learn/nptel/108101371/0666006d542c) (Video)
8. [Lecture 8 - Solution of Ax = b - Part B](https://invisiblenetwork.ai/learn/nptel/108101371/bd5059f35c68) (Video)
9. [Lecture 9 - Solution of Ax = b - Part C](https://invisiblenetwork.ai/learn/nptel/108101371/95b34ba17f2a) (Video)
10. [Lecture 10 - Rings, Integral Domains and Fields - Part A](https://invisiblenetwork.ai/learn/nptel/108101371/4895f9dc5c22) (Video)
11. [Lecture 11 - Rings, Integral Domains and Fields - Part B](https://invisiblenetwork.ai/learn/nptel/108101371/00d12139ecd8) (Video)
12. [Lecture 12 - Rings, Integral Domains and Fields - Part C](https://invisiblenetwork.ai/learn/nptel/108101371/9652e3bf25ef) (Video)
13. [Lecture 13 - Vector Spaces and Subspaces - Part A](https://invisiblenetwork.ai/learn/nptel/108101371/e5e94cb0d874) (Video)
14. [Lecture 14 - Vector Spaces and Subspaces - Part B](https://invisiblenetwork.ai/learn/nptel/108101371/35c388125913) (Video)
15. [Lecture 15 - Vector Spaces and Subspaces - Part C](https://invisiblenetwork.ai/learn/nptel/108101371/530eb02ee1c6) (Video)
16. [Lecture 16 - Unions, Intersection, Sums of Subspaces - Part A](https://invisiblenetwork.ai/learn/nptel/108101371/c9778e2af751) (Video)
17. [Lecture 17 - Unions, Intersection, Sums of Subspaces - Part B](https://invisiblenetwork.ai/learn/nptel/108101371/78bf0e4bd347) (Video)
18. [Lecture 18 - Generating sets, Linear independence and basis - Part A](https://invisiblenetwork.ai/learn/nptel/108101371/dd54e893031b) (Video)
19. [Lecture 19 - Generating sets, Linear independence and basis - Part B](https://invisiblenetwork.ai/learn/nptel/108101371/ff6909a1f973) (Video)
20. [Lecture 20 - Generating sets, Linear independence and basis - Part C](https://invisiblenetwork.ai/learn/nptel/108101371/61706839ddcd) (Video)
21. [Lecture 21 - Ordered basis and co-ordinates - Part A](https://invisiblenetwork.ai/learn/nptel/108101371/075dc35d1b4e) (Video)
22. [Lecture 22 - Ordered basis and co-ordinates - Part B](https://invisiblenetwork.ai/learn/nptel/108101371/6dfa7b6d2927) (Video)
23. [Lecture 23 - Ordered basis and co-ordinates - Part C](https://invisiblenetwork.ai/learn/nptel/108101371/bbefc5743818) (Video)
24. [Lecture 24 - Rank-Nullity Theorem (Matrices) - Part A](https://invisiblenetwork.ai/learn/nptel/108101371/8467aafd48e2) (Video)
25. [Lecture 25 - Rank-Nullity Theorem (Matrices) - Part B](https://invisiblenetwork.ai/learn/nptel/108101371/9e5ec38e8b74) (Video)
26. [Lecture 26 - Rank-Nullity Theorem (Matrices) - Part C](https://invisiblenetwork.ai/learn/nptel/108101371/9a9f0ee38542) (Video)
27. [Lecture 27 - Rank-Nullity Theorem (Linear Transformation) - Part A](https://invisiblenetwork.ai/learn/nptel/108101371/9f452cfe191f) (Video)
28. [Lecture 28 - Rank-Nullity Theorem (Linear Transformation) - Part B](https://invisiblenetwork.ai/learn/nptel/108101371/3d12ad9b9dc9) (Video)
29. [Lecture 29 - Rank-Nullity Theorem (Linear Transformation) - Part C](https://invisiblenetwork.ai/learn/nptel/108101371/57e7d7076bd5) (Video)
30. [Lecture 30 - Isomorphism and Inverses - Part A](https://invisiblenetwork.ai/learn/nptel/108101371/c950f9532463) (Video)
31. [Lecture 31 - Isomorphism and Inverses - Part B](https://invisiblenetwork.ai/learn/nptel/108101371/90388ff47601) (Video)
32. [Lecture 32 - Isomorphism and Inverses - Part C](https://invisiblenetwork.ai/learn/nptel/108101371/7762f7893c13) (Video)
33. [Lecture 33 - Dual Basis and Annihilator - Part A](https://invisiblenetwork.ai/learn/nptel/108101371/58b1d630ffbc) (Video)
34. [Lecture 34 - Dual Basis and Annihilator - Part B](https://invisiblenetwork.ai/learn/nptel/108101371/8cca19be93dc) (Video)
35. [Lecture 35 - Dual Basis and Annihilator - Part C](https://invisiblenetwork.ai/learn/nptel/108101371/ab63ad460c0a) (Video)
36. [Lecture 36 - Dual maps and double dual - Part A](https://invisiblenetwork.ai/learn/nptel/108101371/f796ebaa835d) (Video)
37. [Lecture 37 - Dual maps and double dual - Part B](https://invisiblenetwork.ai/learn/nptel/108101371/42271e491559) (Video)
38. [Lecture 38 - Dual maps and double dual - Part C](https://invisiblenetwork.ai/learn/nptel/108101371/e0a80c10c6d5) (Video)
39. [Lecture 39 - Quotient spaces and quotient map - Part A](https://invisiblenetwork.ai/learn/nptel/108101371/6629ec4a340c) (Video)
40. [Lecture 40 - Quotient spaces and quotient map - Part B](https://invisiblenetwork.ai/learn/nptel/108101371/2f1a7f1bd122) (Video)
41. [Lecture 41 - Quotient spaces and quotient map - Part C](https://invisiblenetwork.ai/learn/nptel/108101371/ac028471c4ba) (Video)
42. [Lecture 42 - Inner Product Spaces - Part A](https://invisiblenetwork.ai/learn/nptel/108101371/d72df9f388ae) (Video)
43. [Lecture 43 - Inner Product Spaces - Part B](https://invisiblenetwork.ai/learn/nptel/108101371/7fe258240d24) (Video)
44. [Lecture 44 - Inner Product Spaces - Part C](https://invisiblenetwork.ai/learn/nptel/108101371/d7ff68ed618b) (Video)
45. [Lecture 45 - Gram Schmidt Procedure - Part A](https://invisiblenetwork.ai/learn/nptel/108101371/fb2ed49f5bd6) (Video)
46. [Lecture 46 - Gram Schmidt Procedure - Part B](https://invisiblenetwork.ai/learn/nptel/108101371/47045819ff3f) (Video)
47. [Lecture 47 - Gram Schmidt Procedure - Part C](https://invisiblenetwork.ai/learn/nptel/108101371/2a0fb3381c2b) (Video)
48. [Lecture 48 - Best Approximation of a Vector - Part A](https://invisiblenetwork.ai/learn/nptel/108101371/d547d6c2361f) (Video)
49. [Lecture 49 - Best Approximation of a Vector - Part B](https://invisiblenetwork.ai/learn/nptel/108101371/a8c65622b686) (Video)
50. [Lecture 50 - Best Approximation of a Vector - Part C](https://invisiblenetwork.ai/learn/nptel/108101371/840adaa9dcad) (Video)
51. [Lecture 51 - Projection map and summary of Ax = b - Part A](https://invisiblenetwork.ai/learn/nptel/108101371/f5e786ea8793) (Video)
52. [Lecture 52 - Projection map and summary of Ax = b - Part B](https://invisiblenetwork.ai/learn/nptel/108101371/8d5e8813f903) (Video)
53. [Lecture 53 - Projection map and summary of Ax = b - Part C](https://invisiblenetwork.ai/learn/nptel/108101371/8310dde8ecd0) (Video)
54. [Lecture 54 - Linear Differential Equations - Part A](https://invisiblenetwork.ai/learn/nptel/108101371/4e2349137751) (Video)
55. [Lecture 55 - Linear Differential Equations - Part B](https://invisiblenetwork.ai/learn/nptel/108101371/1de438a23181) (Video)
56. [Lecture 56 - Introduction to Eigen values and Eigen vectors - Part A](https://invisiblenetwork.ai/learn/nptel/108101371/50af83f0004e) (Video)
57. [Lecture 57 - Introduction to Eigen values and Eigen vectors - Part B](https://invisiblenetwork.ai/learn/nptel/108101371/bcd88ce36e4f) (Video)
58. [Lecture 58 - Introduction to Eigen values and Eigen vectors - Part C](https://invisiblenetwork.ai/learn/nptel/108101371/4f7d531499a5) (Video)
59. [Lecture 59 - Singular Value Decomposition - Part A](https://invisiblenetwork.ai/learn/nptel/108101371/ed51aa6923cc) (Video)
60. [Lecture 60 - Singular Value Decomposition - Part B](https://invisiblenetwork.ai/learn/nptel/108101371/ef2df5d85981) (Video)
61. [Lecture 61 - Singular Value Decomposition - Part C](https://invisiblenetwork.ai/learn/nptel/108101371/2753ff0351a5) (Video)
62. [Lecture 62 - Algebraic and geometric multiplicities - Part A](https://invisiblenetwork.ai/learn/nptel/108101371/b1495f9f0325) (Video)
63. [Lecture 63 - Algebraic and geometric multiplicities - Part B](https://invisiblenetwork.ai/learn/nptel/108101371/a080280d4f12) (Video)
64. [Lecture 64 - A-Invariant Subspaces - Part A](https://invisiblenetwork.ai/learn/nptel/108101371/65e020f61a2e) (Video)
65. [Lecture 65 - A-Invariant Subspaces - Part B](https://invisiblenetwork.ai/learn/nptel/108101371/469688c8a149) (Video)
66. [Lecture 66 - A-Invariant Subspaces - Part C](https://invisiblenetwork.ai/learn/nptel/108101371/1dd38a088a7b) (Video)
67. [Lecture 67 - Minimal Polynomial-I - Part A](https://invisiblenetwork.ai/learn/nptel/108101371/c4459d2874ff) (Video)
68. [Lecture 68 - Minimal Polynomial-I - Part B](https://invisiblenetwork.ai/learn/nptel/108101371/1fbafc29dd34) (Video)
69. [Lecture 69 - Minimal Polynomial-I - Part C](https://invisiblenetwork.ai/learn/nptel/108101371/bd94d7e46fbc) (Video)
70. [Lecture 70 - Minimal Polynomial-I - Part D](https://invisiblenetwork.ai/learn/nptel/108101371/8bc44455871a) (Video)
71. [Lecture 71 - Minimal Polynomial-II - Part A](https://invisiblenetwork.ai/learn/nptel/108101371/4fe3ff7d789e) (Video)
72. [Lecture 72 - Minimal Polynomial-II - Part B](https://invisiblenetwork.ai/learn/nptel/108101371/a95b20704539) (Video)
73. [Lecture 73 - Minimal Polynomial-II - Part C](https://invisiblenetwork.ai/learn/nptel/108101371/f5abc2a4d996) (Video)
74. [Lecture 74 - Minimal Polynomial-II - Part D](https://invisiblenetwork.ai/learn/nptel/108101371/fb56af304350) (Video)
75. [Lecture 75 - Cayley Hamilton Theorem - Part A](https://invisiblenetwork.ai/learn/nptel/108101371/2d84f488f6cc) (Video)
76. [Lecture 76 - Cayley Hamilton Theorem - Part B](https://invisiblenetwork.ai/learn/nptel/108101371/9f4ad42dec6a) (Video)
77. [Lecture 77 - Cayley Hamilton Theorem - Part C](https://invisiblenetwork.ai/learn/nptel/108101371/a4aa307a42c9) (Video)
78. [Lecture 78 - Jordan Canonical Form - Part A](https://invisiblenetwork.ai/learn/nptel/108101371/afa472126617) (Video)
79. [Lecture 79 - Jordan Canonical Form - Part B](https://invisiblenetwork.ai/learn/nptel/108101371/f9cde3181657) (Video)
80. [Lecture 80 - Jordan Canonical Form - Part C](https://invisiblenetwork.ai/learn/nptel/108101371/69f5926cf731) (Video)
81. [Lecture 81 - Algebraic Graph Theory and Consensus - Part A](https://invisiblenetwork.ai/learn/nptel/108101371/43ffbb53edc4) (Video)
82. [Lecture 82 - Algebraic Graph Theory and Consensus - Part B](https://invisiblenetwork.ai/learn/nptel/108101371/6889f0d06c9a) (Video)
83. [Lecture 83 - Algebraic Graph Theory and Consensus - Part C](https://invisiblenetwork.ai/learn/nptel/108101371/7fcc7eeca632) (Video)
84. [Lecture 84 - Positive Matrices and Leontieff's Model - Part A](https://invisiblenetwork.ai/learn/nptel/108101371/09fb2c69883d) (Video)
85. [Lecture 85 - Positive Matrices and Leontieff's Model - Part B](https://invisiblenetwork.ai/learn/nptel/108101371/e60b721686d1) (Video)
86. [Live Session 19-03-2024](https://invisiblenetwork.ai/learn/nptel/108101371/8ad4067b83ea-2) (Video)