# Applied Linear Algebra in AI and ML

- Institution: IIT Kharagpur
- Department: Mathematics
- Teacher: Prof. Swanand Khare
- Level: Undergraduate
- Language: English
- Subjects: Mathematics
- Source: [NPTEL](https://nptel.ac.in/courses/111105165)
- Licence: [CC BY-NC-SA](https://nptel.ac.in/faq) (Non-commercial use only.)
- Syllabus: [at the source](https://nptel.ac.in/courses/111105165)
- Who can watch: Tweens profiles and older (sources give no ratings; placed by Invisible Network from the source's own words)

## Lectures

1. [Lecture 01 : Vector Spaces](https://invisiblenetwork.ai/learn/nptel/111105165/ea3f4c349682) (Video)
2. [Lecture 02 : Vector Subspaces](https://invisiblenetwork.ai/learn/nptel/111105165/41849a605b1e) (Video)
3. [Lecture 03 : Linear Span and Linear Dependence](https://invisiblenetwork.ai/learn/nptel/111105165/0c8957ead794) (Video)
4. [Lecture 04 : Linear Independence](https://invisiblenetwork.ai/learn/nptel/111105165/8acdbe1266c5) (Video)
5. [Lecture 05 : Basis and Dimension](https://invisiblenetwork.ai/learn/nptel/111105165/7aa7be4b0915) (Video)
6. [Lecture 06 : Linear Functionals](https://invisiblenetwork.ai/learn/nptel/111105165/bf06bd7a13cb) (Video)
7. [Lecture 07 : Norm of Vector Part - I](https://invisiblenetwork.ai/learn/nptel/111105165/fc264010eb1f) (Video)
8. [Lecture 08 : Norm of Vector Part - II](https://invisiblenetwork.ai/learn/nptel/111105165/3ef11ee58137) (Video)
9. [Lecture 09 : Linear Functions](https://invisiblenetwork.ai/learn/nptel/111105165/f2ac448547d0) (Video)
10. [Lecture 10 : Affine Functions and Examples](https://invisiblenetwork.ai/learn/nptel/111105165/ddaa1b7ba842) (Video)
11. [Lecture 11: Examples of Linear and Affine Functions](https://invisiblenetwork.ai/learn/nptel/111105165/a80c60b8fac3) (Video)
12. [Lecture 12: Function Composition](https://invisiblenetwork.ai/learn/nptel/111105165/aa8486d6c7b0) (Video)
13. [Lecture 13: System of Linear Equations](https://invisiblenetwork.ai/learn/nptel/111105165/284f83623f0f) (Video)
14. [Lecture 14: Left Invertibility](https://invisiblenetwork.ai/learn/nptel/111105165/353504f6c2c7) (Video)
15. [Lecture 15: Invertibility of Matrices](https://invisiblenetwork.ai/learn/nptel/111105165/8b132533168f) (Video)
16. [Lecture 16: Triangular Systems](https://invisiblenetwork.ai/learn/nptel/111105165/90ecd524996f) (Video)
17. [Lecture 17: LU Decomposition Part - I](https://invisiblenetwork.ai/learn/nptel/111105165/793f83709378) (Video)
18. [Lecture 18: LU Decomposition Part - II](https://invisiblenetwork.ai/learn/nptel/111105165/784160c04455) (Video)
19. [Lecture 19: QR Decomposition (Rotators - Part I)](https://invisiblenetwork.ai/learn/nptel/111105165/2ca84801b564) (Video)
20. [Lecture 20: QR Decomposition (Rotators - Part II)](https://invisiblenetwork.ai/learn/nptel/111105165/c4bac06db057) (Video)
21. [Lecture 21: QR Decomposition (Reflectors - Part I)](https://invisiblenetwork.ai/learn/nptel/111105165/205a8b8805e2) (Video)
22. [Lecture 22: QR Decomposition (Reflectors - Part II)](https://invisiblenetwork.ai/learn/nptel/111105165/9d439d1497aa) (Video)
23. [Lecture 23: Matrix Norms](https://invisiblenetwork.ai/learn/nptel/111105165/8190a66ecdfe) (Video)
24. [Lecture 24: Sensitivity Analysis](https://invisiblenetwork.ai/learn/nptel/111105165/aafb18d0c6eb) (Video)
25. [Lecture 25: Condition Number of a Matrix](https://invisiblenetwork.ai/learn/nptel/111105165/adc0f43540b6) (Video)
26. [Lecture 26: Sensitivity Analysis -II](https://invisiblenetwork.ai/learn/nptel/111105165/d27041573c08) (Video)
27. [Lecture 28: Least Squares - Part I](https://invisiblenetwork.ai/learn/nptel/111105165/6a4400065915) (Video)
28. [Lecture 29: Least Squares - Part II](https://invisiblenetwork.ai/learn/nptel/111105165/0b5589e127cc) (Video)
29. [Lecture 30: Least Squares - Part III](https://invisiblenetwork.ai/learn/nptel/111105165/5184b5f85d26) (Video)
30. [Lecture 31: Least Squares Data Fitting](https://invisiblenetwork.ai/learn/nptel/111105165/0d8e320f032e) (Video)
31. [Lecture 32: Examples of LS data fitting](https://invisiblenetwork.ai/learn/nptel/111105165/f671b1001beb) (Video)
32. [Lecture 33: Classification using Least Squares](https://invisiblenetwork.ai/learn/nptel/111105165/8173a5911c06) (Video)
33. [Lecture 34: Examples of LS classification](https://invisiblenetwork.ai/learn/nptel/111105165/a76204f60790) (Video)
34. [Lecture 35: Constrained Least Squares](https://invisiblenetwork.ai/learn/nptel/111105165/7bb78d301f1d) (Video)
35. [Lecture 36: Multiobjective Least Squares](https://invisiblenetwork.ai/learn/nptel/111105165/66e469165ae8) (Video)
36. [Lecture 37: Eigenvalues and Eigenvectors (Part - I)](https://invisiblenetwork.ai/learn/nptel/111105165/f476139b014f) (Video)
37. [Lecture 38: Eigenvalues and Eigenvectors (Part - II)](https://invisiblenetwork.ai/learn/nptel/111105165/09bb241238f1) (Video)
38. [Lecture 39: Spectral Decomposition Theorem](https://invisiblenetwork.ai/learn/nptel/111105165/d44abeb2ff35) (Video)
39. [Lecture 40: Positive Definite Matrices](https://invisiblenetwork.ai/learn/nptel/111105165/43afb2980230) (Video)
40. [Lecture 27: Sensitivity Analysis -III](https://invisiblenetwork.ai/learn/nptel/111105165/88d62e73379c) (Video)
41. [Lecture 41 : Singular Value Decomposition (SVD)](https://invisiblenetwork.ai/learn/nptel/111105165/4f5a7a053e8f) (Video)
42. [Lecture 42 : Proof of SVD](https://invisiblenetwork.ai/learn/nptel/111105165/879bdfe53932) (Video)
43. [Lecture 43 : Properties of SVD](https://invisiblenetwork.ai/learn/nptel/111105165/54ba745a5c5f) (Video)
44. [Lecture 44 : Another Proof of SVD](https://invisiblenetwork.ai/learn/nptel/111105165/8bdbe30a8287) (Video)
45. [Lecture 45 : Low Rank Approximations](https://invisiblenetwork.ai/learn/nptel/111105165/17decc94e0ac) (Video)
46. [Lecture 46 : Principal Component Analysis](https://invisiblenetwork.ai/learn/nptel/111105165/e52c5d6d58ed) (Video)
47. [Lecture 47 : SVD and Pseudo - Inverse](https://invisiblenetwork.ai/learn/nptel/111105165/0f997ffe3023) (Video)
48. [Lecture 48 : SVD and the Least Squares Problem](https://invisiblenetwork.ai/learn/nptel/111105165/70628f3e93e7) (Video)
49. [Lecture 49 : Sensitivity Analysis of the Least Squares Problem](https://invisiblenetwork.ai/learn/nptel/111105165/e7295b39e139) (Video)
50. [Lecture 50 : Power Method](https://invisiblenetwork.ai/learn/nptel/111105165/c24ebe68ad07) (Video)
51. [Lecture 51 : Directed Graphs and Properties](https://invisiblenetwork.ai/learn/nptel/111105165/9ebfd38295c9) (Video)
52. [Lecture 52 : Page Ranking Algorithm](https://invisiblenetwork.ai/learn/nptel/111105165/b3d2c21a02db) (Video)
53. [Lecture 53 : Inverse Eigen Value Problem](https://invisiblenetwork.ai/learn/nptel/111105165/60efef5a3add) (Video)
54. [Lecture 54 : Fastest Mixing Markov Chains on Graphs (Part I)](https://invisiblenetwork.ai/learn/nptel/111105165/4a01f7393c5e) (Video)
55. [Lecture 55 : Fastest Mixing Markov Chains on Graphs (Part II)](https://invisiblenetwork.ai/learn/nptel/111105165/d206f082129e) (Video)
56. [Lecture 56: Sparse Solution and Underdetermined Systems](https://invisiblenetwork.ai/learn/nptel/111105165/8d35ac30ed6a) (Video)
57. [Lecture 57: Structured Low Rank Approximations (Part I)](https://invisiblenetwork.ai/learn/nptel/111105165/a1853658eeec) (Video)
58. [Lecture 58: Structured Low Rank Approximations (Part II)](https://invisiblenetwork.ai/learn/nptel/111105165/ddd2390d64f2) (Video)
59. [Lecture 59: Structured Low Rank Approximations (Part III)](https://invisiblenetwork.ai/learn/nptel/111105165/5e9c6a854f0f) (Video)
60. [Lecture 60: Recap](https://invisiblenetwork.ai/learn/nptel/111105165/c29323861ea1) (Video)