# Matrix Analysis with Applications

- Institution: IIT Roorkee
- Department: Mathematics
- Taught by: Prof. S. K. Gupta, Prof. Sanjeev Kumar
- Level: Undergraduate
- Language: English
- Subjects: Mathematics
- Source: [NPTEL](https://nptel.ac.in/courses/111107112)
- Licence: [CC BY-NC-SA](https://nptel.ac.in/faq) (Non-commercial use only.)
- Syllabus: [at the source](https://nptel.ac.in/courses/111107112)
- Who can watch: Tweens profiles and older (sources give no ratings; placed by Invisible Network from the source's own words)

This course is offered to UG and PG students of Engineering/Science background. It contains the concepts related to matrix theory and their applications in various disciplines. It covers a depth understanding of matrix computations involving rank, eigenvalues, eigenvectors, linear transformation, similarity transformations, (diagonalisation, Jordan canonical form, etc). It also involves various iterative methods, including Krylov subspace methods. Finally, topics like positive matrices, non-negative matrices and polar decomposition are discussed in detail with their applications.

Intended audience: UG and PG students of technical universities/colleges

## Lectures

1. [Elementary row operations](https://invisiblenetwork.ai/learn/nptel/111107112/38a1a40df286) (YouTube)
2. [Echelon form of a matrix](https://invisiblenetwork.ai/learn/nptel/111107112/76b7b1b0a0ef) (YouTube)
3. [Rank of a matrix](https://invisiblenetwork.ai/learn/nptel/111107112/664c6cdec20c) (YouTube)
4. [System of Linear Equations-I](https://invisiblenetwork.ai/learn/nptel/111107112/39bdcf75d235) (YouTube)
5. [System of Linear Equations-II](https://invisiblenetwork.ai/learn/nptel/111107112/c3e7f5a16291) (YouTube)
6. [Introduction to Vector Spaces](https://invisiblenetwork.ai/learn/nptel/111107112/da2743bd5ee8) (YouTube)
7. [Subspaces](https://invisiblenetwork.ai/learn/nptel/111107112/bbd7707c0fc6) (YouTube)
8. [Basis and Dimension](https://invisiblenetwork.ai/learn/nptel/111107112/d26e491e7521) (YouTube)
9. [Linear Transformations](https://invisiblenetwork.ai/learn/nptel/111107112/58427f433360) (YouTube)
10. [Rank and Nullity](https://invisiblenetwork.ai/learn/nptel/111107112/3a7ef36c0cfe) (YouTube)
11. [Inverse of a Linear Transformation](https://invisiblenetwork.ai/learn/nptel/111107112/b98ac1c521aa) (YouTube)
12. [Matrix Associated with a LT](https://invisiblenetwork.ai/learn/nptel/111107112/85b7342becb3) (YouTube)
13. [Eigenvalues and Eigenvectors](https://invisiblenetwork.ai/learn/nptel/111107112/e8ac1a8107e4) (YouTube)
14. [Cayley-Hamilton Theorem and Minimal Polynomial](https://invisiblenetwork.ai/learn/nptel/111107112/843d80908783) (YouTube)
15. [Diagonalization](https://invisiblenetwork.ai/learn/nptel/111107112/ddfa19570ce8) (YouTube)
16. [Special Matrices](https://invisiblenetwork.ai/learn/nptel/111107112/2fb1c9dccdaf) (YouTube)
17. [More on Special Matrices and Gerschgorin Theorem](https://invisiblenetwork.ai/learn/nptel/111107112/ef9192d0d7c4) (YouTube)
18. [Inner Product Spaces](https://invisiblenetwork.ai/learn/nptel/111107112/ee2ee10dc1e5) (YouTube)
19. [Vector and Matrix Norms](https://invisiblenetwork.ai/learn/nptel/111107112/51b87b12fb8f) (YouTube)
20. [Gram Schmidt Process](https://invisiblenetwork.ai/learn/nptel/111107112/e2e7f5eccd9b) (YouTube)
21. [Normal Matrices](https://invisiblenetwork.ai/learn/nptel/111107112/9d3a6187f960) (YouTube)
22. [Positive Definite Matrices](https://invisiblenetwork.ai/learn/nptel/111107112/88c92ed50e03) (YouTube)
23. [Positive Definite and Quadratic Forms](https://invisiblenetwork.ai/learn/nptel/111107112/2af7d041bc1b) (YouTube)
24. [Gram Matrix and Minimization of Quadratic Forms](https://invisiblenetwork.ai/learn/nptel/111107112/4ab6c705301a) (YouTube)
25. [Generalized Eigenvectors and Jordan Canonical Form](https://invisiblenetwork.ai/learn/nptel/111107112/5317ba7f9dce) (YouTube)
26. [Evaluation of Matrix Functions](https://invisiblenetwork.ai/learn/nptel/111107112/1ba393d2e72a) (YouTube)
27. [Least Square Approximation](https://invisiblenetwork.ai/learn/nptel/111107112/27f884cc877e) (YouTube)
28. [Singular Value Decomposition](https://invisiblenetwork.ai/learn/nptel/111107112/c8434780818b) (YouTube)
29. [Pseudo-Inverse and SVD](https://invisiblenetwork.ai/learn/nptel/111107112/13d1e7b233c1) (YouTube)
30. [Introduction to Ill-Conditioned Systems](https://invisiblenetwork.ai/learn/nptel/111107112/1feea791e56b) (YouTube)
31. [Regularization of Ill-Conditioned Systems](https://invisiblenetwork.ai/learn/nptel/111107112/feb75d92198a) (YouTube)
32. [Linear Systems : Iterative Methods I](https://invisiblenetwork.ai/learn/nptel/111107112/7dc11fa44d89) (YouTube)
33. [Linear Systems : Iterative Methods II](https://invisiblenetwork.ai/learn/nptel/111107112/dd54e18055e4) (YouTube)
34. [Non-Stationary Iterative Methods: Steepest Descent-I](https://invisiblenetwork.ai/learn/nptel/111107112/1339a8f8a417) (YouTube)
35. [Non-Stationary Iterative Methods: Steepest Descent-II](https://invisiblenetwork.ai/learn/nptel/111107112/4c1a60e95271) (YouTube)
36. [Krylov Subspace Iterative Methods (Conjugate Gradient Method)](https://invisiblenetwork.ai/learn/nptel/111107112/a9d04de5145e) (YouTube)
37. [Krylov Subspace Iterative Methods (CG and Pre-Conditioning)](https://invisiblenetwork.ai/learn/nptel/111107112/ae9e4e867800) (YouTube)
38. [Introduction to Positive Matrices](https://invisiblenetwork.ai/learn/nptel/111107112/92a90ceb0a60) (YouTube)
39. [Non-Negativity and Irreducible Matrices](https://invisiblenetwork.ai/learn/nptel/111107112/9d40034a7d6d) (YouTube)
40. [Polar Decomposition](https://invisiblenetwork.ai/learn/nptel/111107112/b7d027f3d9d1) (YouTube)