# Linear Algebra

- Institution: IIT Kanpur
- Department: Mathematics
- Teacher: Prof. Arbind Kumar Lal
- Level: Undergraduate
- Language: English
- Subjects: Mathematics
- Source: [NPTEL](https://nptel.ac.in/courses/111104137)
- Licence: [CC BY-NC-SA](https://nptel.ac.in/faq) (Non-commercial use only.)
- Syllabus: [at the source](https://nptel.ac.in/courses/111104137)
- Who can watch: Tweens profiles and older (sources give no ratings; placed by Invisible Network from the source's own words)

## Lectures

1. [Notations, Motivation and Definition](https://invisiblenetwork.ai/learn/nptel/111104137/cbdc788aebd3) (Video)
2. [Matrix: Examples, Transpose and Addition](https://invisiblenetwork.ai/learn/nptel/111104137/f1491b558f11) (Video)
3. [Matrix Multiplication](https://invisiblenetwork.ai/learn/nptel/111104137/e39b2371021d) (Video)
4. [Matrix Product Recalled](https://invisiblenetwork.ai/learn/nptel/111104137/f4c430cbdda6) (Video)
5. [Matrix Product Continued](https://invisiblenetwork.ai/learn/nptel/111104137/cf3d7d44efc8) (Video)
6. [Inverse of a Matrix](https://invisiblenetwork.ai/learn/nptel/111104137/98ef28466e8b) (Video)
7. [Introduction to System of Linear Equations](https://invisiblenetwork.ai/learn/nptel/111104137/a1d3b822ecff) (Video)
8. [Some Initial Results on Linear Systems](https://invisiblenetwork.ai/learn/nptel/111104137/5bba8699aa9b) (Video)
9. [Row Echelon Form (REF)](https://invisiblenetwork.ai/learn/nptel/111104137/483607bec6f8) (Video)
10. [LU Decomposition - Simplest Form](https://invisiblenetwork.ai/learn/nptel/111104137/5ade482194c0) (Video)
11. [Elementary Matrices](https://invisiblenetwork.ai/learn/nptel/111104137/3925372e2ddf) (Video)
12. [Row Reduced Echelon Form (RREF)](https://invisiblenetwork.ai/learn/nptel/111104137/c42170461bf6) (Video)
13. [Row Reduced Echelon Form (RREF) Continued](https://invisiblenetwork.ai/learn/nptel/111104137/913bd14b7265) (Video)
14. [RREF and Inverse](https://invisiblenetwork.ai/learn/nptel/111104137/27ca5929e64f) (Video)
15. [Rank of a matrix](https://invisiblenetwork.ai/learn/nptel/111104137/3d9b7f90b1d8) (Video)
16. [Solution Set of a System of Linear Equations](https://invisiblenetwork.ai/learn/nptel/111104137/22be7969a683) (Video)
17. [System of n Linear Equations in n Unknowns](https://invisiblenetwork.ai/learn/nptel/111104137/4a435735069c) (Video)
18. [Determinant](https://invisiblenetwork.ai/learn/nptel/111104137/80927ca2e395) (Video)
19. [Permutations and the Inverse of a Matrix](https://invisiblenetwork.ai/learn/nptel/111104137/c873d960e13f) (Video)
20. [Inverse and the Cramer's Rule](https://invisiblenetwork.ai/learn/nptel/111104137/436f8f81c48f) (Video)
21. [Vector Spaces](https://invisiblenetwork.ai/learn/nptel/111104137/876a1304ceb6) (Video)
22. [Vector Subspaces and Linear Span](https://invisiblenetwork.ai/learn/nptel/111104137/3085e3a4acb1) (Video)
23. [Linear Combination, Linear Independence and Dependence](https://invisiblenetwork.ai/learn/nptel/111104137/48ea3fabbf8b) (Video)
24. [Basic Results on Linear Independence](https://invisiblenetwork.ai/learn/nptel/111104137/c4e4796d860c) (Video)
25. [Results on Linear Independence Continued...](https://invisiblenetwork.ai/learn/nptel/111104137/aa88d630c998) (Video)
26. [Basis of a Finite Dimensional Vector Space](https://invisiblenetwork.ai/learn/nptel/111104137/338f6b04edcc) (Video)
27. [Fundamental Spaces associated with a Matrix](https://invisiblenetwork.ai/learn/nptel/111104137/f76f40ad060f) (Video)
28. [Rank - Nullity Theorem](https://invisiblenetwork.ai/learn/nptel/111104137/ee22e82302fc) (Video)
29. [Fundamental Theorem of Linear Algebra](https://invisiblenetwork.ai/learn/nptel/111104137/419465f41c39) (Video)
30. [Definition and Examples of Linear Transformations](https://invisiblenetwork.ai/learn/nptel/111104137/ad8deda00b64) (Video)
31. [Results on Linear Transformations](https://invisiblenetwork.ai/learn/nptel/111104137/2e44cab11930) (Video)
32. [Rank-Nullity Theorem and Applications](https://invisiblenetwork.ai/learn/nptel/111104137/04df17674479) (Video)
33. [Isomorphism of Vector Spaces](https://invisiblenetwork.ai/learn/nptel/111104137/447f90259cbf) (Video)
34. [Ordered Basis of a Finite Dimensional Vector Space](https://invisiblenetwork.ai/learn/nptel/111104137/69fcdfe665e1) (Video)
35. [Ordered Basis Continued](https://invisiblenetwork.ai/learn/nptel/111104137/d8ca023162c3) (YouTube)
36. [Matrix of a Linear transformation](https://invisiblenetwork.ai/learn/nptel/111104137/81b0b356fc58) (YouTube)
37. [Matrix of a Linear transformation Continued...](https://invisiblenetwork.ai/learn/nptel/111104137/b6b8900cc4e9) (YouTube)
38. [Matrix of Linear Transformations Continued...](https://invisiblenetwork.ai/learn/nptel/111104137/8f194ad19bea) (YouTube)
39. [Similarity of Matrices](https://invisiblenetwork.ai/learn/nptel/111104137/e75ea56e2084) (YouTube)
40. [Inner Product Space](https://invisiblenetwork.ai/learn/nptel/111104137/fed959c7db3c) (YouTube)
41. [Inner Product Continued](https://invisiblenetwork.ai/learn/nptel/111104137/9d959cf2ba76) (YouTube)
42. [Cauchy Schwartz Inequality](https://invisiblenetwork.ai/learn/nptel/111104137/1aa5b904124b) (YouTube)
43. [Projection on a Vector](https://invisiblenetwork.ai/learn/nptel/111104137/5e7e963e12a8) (YouTube)
44. [Results on Orthogonality](https://invisiblenetwork.ai/learn/nptel/111104137/d72eddb4a5ff) (YouTube)
45. [Results on Orthogonality.](https://invisiblenetwork.ai/learn/nptel/111104137/ce3fe0f99e02) (YouTube)
46. [Gram-Schmidt Orthonormalization Process](https://invisiblenetwork.ai/learn/nptel/111104137/b1be159280dd) (YouTube)
47. [Orthogonal Projections](https://invisiblenetwork.ai/learn/nptel/111104137/1bf807f1901e) (YouTube)
48. [Gram-Schmidt Process: Applications](https://invisiblenetwork.ai/learn/nptel/111104137/64d7b1e37b96) (YouTube)
49. [Examples and Applications on QR-decomposition](https://invisiblenetwork.ai/learn/nptel/111104137/4471a3f5b1c0) (YouTube)
50. [Recapitulate ideas on Inner Product Spaces](https://invisiblenetwork.ai/learn/nptel/111104137/6202d0bf03f8) (YouTube)
51. [Motivation on Eigenvalues and Eigenvectors](https://invisiblenetwork.ai/learn/nptel/111104137/b98c5d47c344) (YouTube)
52. [Examples and Introduction to Eigenvalues and Eigenvectors](https://invisiblenetwork.ai/learn/nptel/111104137/b62f6e3678b5) (YouTube)
53. [Results on Eigenvalues and Eigenvectors](https://invisiblenetwork.ai/learn/nptel/111104137/e27595ecbb28) (YouTube)
54. [Results on Eigenvalues and Eigenvectors](https://invisiblenetwork.ai/learn/nptel/111104137/923c01684ffb) (YouTube)
55. [Results on Eigenvalues and Eigenvectors.](https://invisiblenetwork.ai/learn/nptel/111104137/66cbbcdb20cb) (YouTube)
56. [Diagonalizability](https://invisiblenetwork.ai/learn/nptel/111104137/9439a2d2a177) (YouTube)
57. [Diagonalizability Continued...](https://invisiblenetwork.ai/learn/nptel/111104137/1787a2ea3caf) (YouTube)
58. [Schur's Unitary Triangularization (SUT)](https://invisiblenetwork.ai/learn/nptel/111104137/51104928cea1) (YouTube)
59. [Applications of Schur's Unitary Triangularization](https://invisiblenetwork.ai/learn/nptel/111104137/b06d941bd55e) (YouTube)
60. [Spectral Theorem for Hermitian Matrices](https://invisiblenetwork.ai/learn/nptel/111104137/d88d2deed910) (YouTube)
61. [Cayley Hamilton Theorem](https://invisiblenetwork.ai/learn/nptel/111104137/7e656cf6510e) (YouTube)
62. [Quadratic Forms](https://invisiblenetwork.ai/learn/nptel/111104137/b4bb40f07d10) (YouTube)
63. [Sylvester's Law of Inertia](https://invisiblenetwork.ai/learn/nptel/111104137/b5cea0d76284) (YouTube)
64. [Applications of Quadratic Forms to Analytic Geometry](https://invisiblenetwork.ai/learn/nptel/111104137/3b868314a9c3) (YouTube)
65. [Examples of Conics and Quartics](https://invisiblenetwork.ai/learn/nptel/111104137/e9fac0f7a8a8) (YouTube)
66. [Singular Value Decomposition (SVD)](https://invisiblenetwork.ai/learn/nptel/111104137/76727922adaf) (YouTube)
67. [Live Session 20-10-2020](https://invisiblenetwork.ai/learn/nptel/111104137/cbdc788aebd3-2) (Video)