# Applied Linear Algebra

- Institution: IIT Madras
- Department: Electrical Engineering
- Teacher: Prof. Andrew Thangaraj
- Level: Undergraduate
- Language: English
- Subjects: Engineering
- Source: [NPTEL](https://nptel.ac.in/courses/108106171)
- Licence: [CC BY-NC-SA](https://nptel.ac.in/faq) (Non-commercial use only.)
- Syllabus: [at the source](https://nptel.ac.in/courses/108106171)
- Who can watch: Tweens profiles and older (sources give no ratings; placed by Invisible Network from the source's own words)

## Lectures

1. [Introduction to the Course](https://invisiblenetwork.ai/learn/nptel/108106171/9942c632b225) (Video)
2. [Vector Spaces: Introduction](https://invisiblenetwork.ai/learn/nptel/108106171/3e5c481b2b1a) (Video)
3. [Linear Combinations and Span](https://invisiblenetwork.ai/learn/nptel/108106171/c8a72abee2f9) (Video)
4. [Subspaces, Linear Dependence and Independence](https://invisiblenetwork.ai/learn/nptel/108106171/8fef606c78f3) (Video)
5. [Basis and Dimension](https://invisiblenetwork.ai/learn/nptel/108106171/bc39a7e71a15) (Video)
6. [Sums, Direct Sums and Gaussian Elimination](https://invisiblenetwork.ai/learn/nptel/108106171/e7fc4b7b9ca9) (Video)
7. [Linear Maps and Matrices](https://invisiblenetwork.ai/learn/nptel/108106171/52a3da4891a0) (Video)
8. [Null space, Range, Fundamental theorem of linear maps](https://invisiblenetwork.ai/learn/nptel/108106171/c3a335bb6919) (Video)
9. [Column space, null space and rank of a matrix](https://invisiblenetwork.ai/learn/nptel/108106171/43db020868a1) (Video)
10. [Algebraic operations on linear maps](https://invisiblenetwork.ai/learn/nptel/108106171/8a361921c64f) (Video)
11. [Invertible maps, Isomorphism, Operators](https://invisiblenetwork.ai/learn/nptel/108106171/4f391f64a946) (Video)
12. [Solving Linear Equations](https://invisiblenetwork.ai/learn/nptel/108106171/077637c1f414) (Video)
13. [Elementary Row Operations](https://invisiblenetwork.ai/learn/nptel/108106171/79110df1da71) (Video)
14. [Translates of a subspace, Quotient Spaces](https://invisiblenetwork.ai/learn/nptel/108106171/bb5a8c96cb56) (Video)
15. [Row space and rank of a matrix](https://invisiblenetwork.ai/learn/nptel/108106171/bbcd2de61034) (Video)
16. [Determinants](https://invisiblenetwork.ai/learn/nptel/108106171/d6506a43a16d) (Video)
17. [Coordinates and linear maps under a change of basis](https://invisiblenetwork.ai/learn/nptel/108106171/e1c9f8510a3c) (Video)
18. [Simplifying matrices of linear maps by choice of basis](https://invisiblenetwork.ai/learn/nptel/108106171/f9e0ed90c286) (Video)
19. [Polynomials and Roots](https://invisiblenetwork.ai/learn/nptel/108106171/654eafcdbdc6) (Video)
20. [Invariant subspaces, Eigenvalues, Eigenvectors](https://invisiblenetwork.ai/learn/nptel/108106171/67e0c69284e7) (Video)
21. [More on Eigenvalues, Eigenvectors, Diagonalization](https://invisiblenetwork.ai/learn/nptel/108106171/6300ab84d880) (Video)
22. [Eigenvalues, Eigenvectors and Upper Triangularization](https://invisiblenetwork.ai/learn/nptel/108106171/626cc98535ae) (Video)
23. [Properties of Eigenvalues](https://invisiblenetwork.ai/learn/nptel/108106171/fd956a4c908b) (Video)
24. [Linear state space equations and system stability](https://invisiblenetwork.ai/learn/nptel/108106171/9ed4df567db1) (Video)
25. [Discrete-time Linear Systems and Discrete Fourier Transforms](https://invisiblenetwork.ai/learn/nptel/108106171/ffa5b2f33cc1) (Video)
26. [Sequences and counting paths in graphs](https://invisiblenetwork.ai/learn/nptel/108106171/9f6438d3412e) (Video)
27. [PageRank Algorithm](https://invisiblenetwork.ai/learn/nptel/108106171/7b4bd394705f) (Video)
28. [Dot product and length in Cn, Inner product and norm in V over F](https://invisiblenetwork.ai/learn/nptel/108106171/70eb7ba10a65) (Video)
29. [Orthonormal basis and Gram-Schmidt orthogonalisation](https://invisiblenetwork.ai/learn/nptel/108106171/d25be1f53eb7) (Video)
30. [Linear Functionals, Orthogonal Complements](https://invisiblenetwork.ai/learn/nptel/108106171/47414e0ff3da) (Video)
31. [Orthogonal Projection](https://invisiblenetwork.ai/learn/nptel/108106171/2583ff97612e) (Video)
32. [Projection and distance from a subspace](https://invisiblenetwork.ai/learn/nptel/108106171/81d885677dad) (Video)
33. [Linear equations, Least squares solutions and Linear regression](https://invisiblenetwork.ai/learn/nptel/108106171/aba66d703e4a) (Video)
34. [Minimum Mean Squared Error Estimation](https://invisiblenetwork.ai/learn/nptel/108106171/9108f0124490) (Video)
35. [Adjoint of a linear map](https://invisiblenetwork.ai/learn/nptel/108106171/1e8043bdf949) (Video)
36. [Properties of Adjoint of a Linear Map](https://invisiblenetwork.ai/learn/nptel/108106171/a2fb68f10f17) (Video)
37. [Adjoint of an Operator and Operator-Adjoint Product](https://invisiblenetwork.ai/learn/nptel/108106171/862ad0cc297f) (Video)
38. [Self-adjoint Operator](https://invisiblenetwork.ai/learn/nptel/108106171/83e4c54c8e50) (Video)
39. [Normal Operators](https://invisiblenetwork.ai/learn/nptel/108106171/37d65db5470d) (Video)
40. [Complex Spectral Theorem](https://invisiblenetwork.ai/learn/nptel/108106171/4022b75940c1) (Video)
41. [Real Spectral Theorem](https://invisiblenetwork.ai/learn/nptel/108106171/6a3566eed0f2) (Video)
42. [Positive Operators](https://invisiblenetwork.ai/learn/nptel/108106171/9c077391464a) (Video)
43. [Quadratic Forms, Matrix Norms and Optimization](https://invisiblenetwork.ai/learn/nptel/108106171/67af479924b0) (Video)
44. [Isometries](https://invisiblenetwork.ai/learn/nptel/108106171/804258ece1ba) (Video)
45. [Classification of Operators](https://invisiblenetwork.ai/learn/nptel/108106171/e35a281db11f) (Video)
46. [Singular Values and Vectors of a Linear Map](https://invisiblenetwork.ai/learn/nptel/108106171/36325c436540) (Video)
47. [Singular Value Decomposition](https://invisiblenetwork.ai/learn/nptel/108106171/37f3eb68480f) (Video)
48. [Polar decomposition and some applications of SVD](https://invisiblenetwork.ai/learn/nptel/108106171/15ca390575ee) (Video)
49. [Live Session 15-04-2021](https://invisiblenetwork.ai/learn/nptel/108106171/9942c632b225-2) (Video)
50. [Live Session 19-04-2021](https://invisiblenetwork.ai/learn/nptel/108106171/3e5c481b2b1a-2) (Video)
51. [Live Session 19-04-2022](https://invisiblenetwork.ai/learn/nptel/108106171/c8a72abee2f9-2) (Video)