# Matrix Computation and its applications - Institution: IIT Delhi - Department: Mathematics - Taught by: Prof. Mani Mehra, Prof. Vivek Kumar Aggarwal - Level: Undergraduate - Language: English - Subjects: Mathematics - Source: [NPTEL](https://nptel.ac.in/courses/111102152) - Licence: [CC BY-NC-SA](https://nptel.ac.in/faq) (Non-commercial use only.) - Syllabus: [at the source](https://nptel.ac.in/courses/111102152) - Who can watch: Tweens profiles and older (sources give no ratings; placed by Invisible Network from the source's own words) This course deals with applications of matrices to a wide range of areas of engineering and science. Initial some basics of linear algebra is discussed followed by matrix norms and sensitivity and condition number of the matrices. In this course , we will also discuss psudo-inverse of a matrix of any dimension (m x n) using Moore- Penrose theorem. Singular value decomposition of a general matrix is also discussed along with applications. Householder transformations, QR factorization will also be covered. Intended audience: UG/PG Prerequisites: Some knowledge of matrix theory ## Lectures 1. [Binary Operation and Groups](https://invisiblenetwork.ai/learn/nptel/111102152/3cc563fdb193) (YouTube) 2. [Vector Spaces](https://invisiblenetwork.ai/learn/nptel/111102152/c039630d6db7) (YouTube) 3. [Some Example of Vector Spaces](https://invisiblenetwork.ai/learn/nptel/111102152/7c237be2a06d) (YouTube) 4. [Some Example of Vector Spaces (contd.)](https://invisiblenetwork.ai/learn/nptel/111102152/93bdfae166b9) (YouTube) 5. [Subspace of a Vector Space](https://invisiblenetwork.ai/learn/nptel/111102152/18cfd4e7a8ef) (YouTube) 6. [Spanning Set](https://invisiblenetwork.ai/learn/nptel/111102152/7d20cc5fdb79) (YouTube) 7. [Properties of Subspace](https://invisiblenetwork.ai/learn/nptel/111102152/74a57c717707) (YouTube) 8. [Properties of Subspace (contd.)](https://invisiblenetwork.ai/learn/nptel/111102152/82db38a835a9) (YouTube) 9. [Linearly independent and dependent vectors](https://invisiblenetwork.ai/learn/nptel/111102152/297bec86c21b) (YouTube) 10. [Linearly independent and dependent vectors (contd.)](https://invisiblenetwork.ai/learn/nptel/111102152/64ed0773642f) (YouTube) 11. [Properties of linearly independent and dependent vectors](https://invisiblenetwork.ai/learn/nptel/111102152/3aafaf20e19d) (YouTube) 12. [Properties of linearly independent and dependent vectors (contd.)](https://invisiblenetwork.ai/learn/nptel/111102152/49ba027cb95e) (YouTube) 13. [Basis and Dimension of a Vector Space](https://invisiblenetwork.ai/learn/nptel/111102152/137c4a44453e) (YouTube) 14. [Examples of Basis and standard basis of a vector space](https://invisiblenetwork.ai/learn/nptel/111102152/a5917cb2fc50) (YouTube) 15. [Linear Functions](https://invisiblenetwork.ai/learn/nptel/111102152/c9cda2d6d08e) (YouTube) 16. [Range space of a matrix and row reduced echelon form](https://invisiblenetwork.ai/learn/nptel/111102152/0e5307412778) (YouTube) 17. [Row equivalent matrices](https://invisiblenetwork.ai/learn/nptel/111102152/eea002532771) (YouTube) 18. [Row equivalent matrices (contd.)](https://invisiblenetwork.ai/learn/nptel/111102152/f63b48ddfc58) (YouTube) 19. [Null Space of a Matrix](https://invisiblenetwork.ai/learn/nptel/111102152/555f8c7e4bc2) (YouTube) 20. [Four subspaces associated with a given matrix](https://invisiblenetwork.ai/learn/nptel/111102152/5e776fb62530) (YouTube) 21. [Four subspaces associated with a given matrix (contd.)](https://invisiblenetwork.ai/learn/nptel/111102152/4ee9ea58ccd6) (YouTube) 22. [Linear Independence of the rows and columns of a matrix](https://invisiblenetwork.ai/learn/nptel/111102152/746abb18fbde) (YouTube) 23. [Application of diagonal dominant matrices](https://invisiblenetwork.ai/learn/nptel/111102152/f4ecf606554a) (YouTube) 24. [Application of Zero Null space: Interpolating polynomial and wronskian matrix](https://invisiblenetwork.ai/learn/nptel/111102152/165dedf1a68a) (YouTube) 25. [Characterization of basis of a vector space and its subspaces](https://invisiblenetwork.ai/learn/nptel/111102152/a0f9812f9bc3) (YouTube) 26. [Coordinate of a vector with respect to ordered basis](https://invisiblenetwork.ai/learn/nptel/111102152/8f015f3599c1) (YouTube) 27. [Examples of different subspaces of a vector space of polynomials having degree less than or equal to 3](https://invisiblenetwork.ai/learn/nptel/111102152/578808ed19e4) (YouTube) 28. [Linear transformation](https://invisiblenetwork.ai/learn/nptel/111102152/d76758f5c5f8) (YouTube) 29. [Properties of linear transformation](https://invisiblenetwork.ai/learn/nptel/111102152/9f7315009f49) (YouTube) 30. [Determining linear transformation on a vector space by its value on the basis element](https://invisiblenetwork.ai/learn/nptel/111102152/b0facde6ff58) (YouTube) 31. [Range space and null space of a linear transformation](https://invisiblenetwork.ai/learn/nptel/111102152/8d0b7caed8c1) (YouTube) 32. [Rank and nuility of a linear transformation](https://invisiblenetwork.ai/learn/nptel/111102152/895bf79a9e9c) (YouTube) 33. [Rank-nuility theorem](https://invisiblenetwork.ai/learn/nptel/111102152/b1a98b301764) (YouTube) 34. [Application of rank-nuility theorem and inverse of a linear transformation](https://invisiblenetwork.ai/learn/nptel/111102152/500e157c5b12) (YouTube) 35. [Matrix associated with linear transformation](https://invisiblenetwork.ai/learn/nptel/111102152/9c469340b131) (YouTube) 36. [Matrix representation of a linear transformation relative to ordered bases](https://invisiblenetwork.ai/learn/nptel/111102152/309d7e402ea9) (YouTube) 37. [Matrix representation of a linear transformation relative to ordered bases (contd.)](https://invisiblenetwork.ai/learn/nptel/111102152/d52cbe6f3ae6) (YouTube) 38. [Linear map associated with a matrix](https://invisiblenetwork.ai/learn/nptel/111102152/f03253ed8f75) (YouTube) 39. [Similar matrices and diagonalisation of matrix](https://invisiblenetwork.ai/learn/nptel/111102152/91c703ae9f27) (YouTube) 40. [Orthonormal bases of a vector space](https://invisiblenetwork.ai/learn/nptel/111102152/7074d4671d0b) (YouTube) 41. [Gram-Schmidt orthogonalisation process](https://invisiblenetwork.ai/learn/nptel/111102152/1b4315e98dd3) (YouTube) 42. [QR factorisation](https://invisiblenetwork.ai/learn/nptel/111102152/c86e7787b0fd) (YouTube) 43. [Inner Product Spaces](https://invisiblenetwork.ai/learn/nptel/111102152/d7d47bc6131c) (YouTube) 44. [Inner product on different real vector spaces and basis of complex vector space](https://invisiblenetwork.ai/learn/nptel/111102152/3768a2550197) (YouTube) 45. [Inner product on complex vector spaces and Cauchy-Schwarz inequality](https://invisiblenetwork.ai/learn/nptel/111102152/beac1347c60e) (YouTube) 46. [Norm of a vector](https://invisiblenetwork.ai/learn/nptel/111102152/bd7bf51f0e2e) (YouTube) 47. [Matrix norm](https://invisiblenetwork.ai/learn/nptel/111102152/e09a931d1a8e) (YouTube) 48. [Sensitivity analysis of a system of linear equations](https://invisiblenetwork.ai/learn/nptel/111102152/888b53b87e4a) (YouTube) 49. [Orthogonality of the four subspaces associated with a Matrix](https://invisiblenetwork.ai/learn/nptel/111102152/d7b79e7382f0) (YouTube) 50. [Best approximation : Least square method](https://invisiblenetwork.ai/learn/nptel/111102152/6c3eb4965c7e) (YouTube) 51. [Best approximation : Least square method (contd.)](https://invisiblenetwork.ai/learn/nptel/111102152/d25cc8e3c1c3) (YouTube) 52. [Jordan-Canonical Form](https://invisiblenetwork.ai/learn/nptel/111102152/157fe5174aa0) (YouTube) 53. [Some examples on the Jordan form of a given matrix and generalised eigenvectors](https://invisiblenetwork.ai/learn/nptel/111102152/0d9c9dcc43b3) (YouTube) 54. [Singular value decomposition (SVD) theorem](https://invisiblenetwork.ai/learn/nptel/111102152/191dfc53c3b4) (YouTube) 55. [Matlab / Octave code for solving SVD](https://invisiblenetwork.ai/learn/nptel/111102152/43fccd3842cb) (YouTube) 56. [Pseudo-inverse/Moore-Penrose inverse](https://invisiblenetwork.ai/learn/nptel/111102152/af07e36b1fdf) (YouTube) 57. [Householder transformation](https://invisiblenetwork.ai/learn/nptel/111102152/90a6b0000f31) (YouTube) 58. [Matlab/Octave code for Householder transformation](https://invisiblenetwork.ai/learn/nptel/111102152/316519ce76aa) (YouTube)