| Sl.No | Chapter Name | MP4 Download |
|---|---|---|
| 1 | Course introduction and properties of matrices | Download |
| 2 | Vector spaces | Download |
| 3 | Basis, dimension | Download |
| 4 | Linear transforms | Download |
| 5 | Fundamental subspaces of a matrix | Download |
| 6 | Fundamental theorem of linear algebra | Download |
| 7 | Properties of rank | Download |
| 8 | Inner product | Download |
| 9 | Gram-schmidt algorithm | Download |
| 10 | Orthonormal matrices definition | Download |
| 11 | Determinant | Download |
| 12 | Properties of determinants | Download |
| 13 | Introduction to norms and inner products | Download |
| 14 | Vector norms and their properties, | Download |
| 15 | Applications and equivalence of vector norms | Download |
| 16 | Summary of equivalence of norms | Download |
| 17 | Dual norms | Download |
| 18 | Properties and examples of dual norms | Download |
| 19 | Matrix norms | Download |
| 20 | Matrix norms: Properties | Download |
| 21 | Induced norms | Download |
| 22 | Induced norms and examples | Download |
| 23 | Spectral radius | Download |
| 24 | Properties of spectral radius | Download |
| 25 | Convergent matrices, Banach lemma | Download |
| 26 | Recap of matrix norms and Levy-Desplanques theorem | Download |
| 27 | Equivalence of matrix norms and error in inverses of linear systems | Download |
| 28 | Errors in inverses of matrices | Download |
| 29 | Errors in solving systems of linear equations | Download |
| 30 | Introduction to eigenvalues and eigenvectors | Download |
| 31 | The characteristic polynomial | Download |
| 32 | Solving characteristic polynomials, eigenvectors properties | Download |
| 33 | Similarity | Download |
| 34 | Diagonalization | Download |
| 35 | Relationship between eigenvalues of BA and AB | Download |
| 36 | Eigenvector and principle of biorthogonality | Download |
| 37 | Unitary matrices | Download |
| 38 | Properties of unitary matrices | Download |
| 39 | Unitary equivalence | Download |
| 40 | Schur's triangularization theorem | Download |
| 41 | Cayley-Hamilton theorem | Download |
| 42 | Uses of cayley-hamilton theorem and diagonalizability revisited | Download |
| 43 | Normal matrices: Definition and fundamental properties | Download |
| 44 | Fundamental properties of normal matrices | Download |
| 45 | QR decomposition and canonical forms | Download |
| 46 | Jordan canonical form | Download |
| 47 | Determining the Jordan form of a matrix | Download |
| 48 | Properties of the Jordan canonical form (part 1) | Download |
| 49 | Properties of the Jordan canonical form (part 2) | Download |
| 50 | Properties of convergent matrices | Download |
| 51 | Polynomials and matrices | Download |
| 52 | Other canonical forms and factorization of matrices: Gaussian elimination & LU factorization | Download |
| 53 | LU decomposition | Download |
| 54 | LU decomposition with pivoting | Download |
| 55 | Solving pivoted system and LDM decomposition | Download |
| 56 | Cholesky decomposition and uses | Download |
| 57 | Hermitian and symmetric matrix | Download |
| 58 | Properties of hermitian matrices | Download |
| 59 | Variational characterization of Eigenvalues: Rayleigh-Ritz theorem | Download |
| 60 | Variational characterization of eigenvalues (continued) | Download |
| 61 | Courant-Fischer theorem | Download |
| 62 | Summary of Rayliegh-Ritz and Courant-Fischer theorems | Download |
| 63 | Weyl's theorem | Download |
| 64 | Positive semi-definite matrix, monotonicity theorem and interlacing theorems | Download |
| 65 | Interlacing theorem I | Download |
| 66 | Interlacing theorem II (Converse) | Download |
| 67 | Interlacing theorem (Continued) | Download |
| 68 | Eigenvalues: Majorization theorem and proof | Download |
| 69 | Location and perturbation of Eigenvalues Part1: Dominant diagonal theorem | Download |
| 70 | Location and perturbation of Eigenvalues Part2: Gersgorin's theorem | Download |
| 71 | Implications of Gersgorin disc theorem, condition of eigenvalues | Download |
| 72 | Condition of eigenvalues for diagonalizable matrices | Download |
| 73 | Perturbation of eigenvalues Birkhoff's theorem Hoffman - Weilandt theorem | Download |
| 74 | Singular value definition and some remarks. | Download |
| 75 | Proof of singular value decomposition theorem. | Download |
| 76 | Partitioning the SVD | Download |
| 77 | Properties of SVD | Download |
| 78 | Generalized inverse of matrices | Download |
| 79 | Least squares | Download |
| 80 | Constrained least squares | Download |
| Sl.No | Chapter Name | English |
|---|---|---|
| 1 | Course introduction and properties of matrices | PDF unavailable |
| 2 | Vector spaces | PDF unavailable |
| 3 | Basis, dimension | PDF unavailable |
| 4 | Linear transforms | PDF unavailable |
| 5 | Fundamental subspaces of a matrix | PDF unavailable |
| 6 | Fundamental theorem of linear algebra | PDF unavailable |
| 7 | Properties of rank | PDF unavailable |
| 8 | Inner product | PDF unavailable |
| 9 | Gram-schmidt algorithm | PDF unavailable |
| 10 | Orthonormal matrices definition | PDF unavailable |
| 11 | Determinant | PDF unavailable |
| 12 | Properties of determinants | PDF unavailable |
| 13 | Introduction to norms and inner products | PDF unavailable |
| 14 | Vector norms and their properties, | PDF unavailable |
| 15 | Applications and equivalence of vector norms | PDF unavailable |
| 16 | Summary of equivalence of norms | PDF unavailable |
| 17 | Dual norms | PDF unavailable |
| 18 | Properties and examples of dual norms | PDF unavailable |
| 19 | Matrix norms | PDF unavailable |
| 20 | Matrix norms: Properties | PDF unavailable |
| 21 | Induced norms | PDF unavailable |
| 22 | Induced norms and examples | PDF unavailable |
| 23 | Spectral radius | PDF unavailable |
| 24 | Properties of spectral radius | PDF unavailable |
| 25 | Convergent matrices, Banach lemma | PDF unavailable |
| 26 | Recap of matrix norms and Levy-Desplanques theorem | PDF unavailable |
| 27 | Equivalence of matrix norms and error in inverses of linear systems | PDF unavailable |
| 28 | Errors in inverses of matrices | PDF unavailable |
| 29 | Errors in solving systems of linear equations | PDF unavailable |
| 30 | Introduction to eigenvalues and eigenvectors | PDF unavailable |
| 31 | The characteristic polynomial | PDF unavailable |
| 32 | Solving characteristic polynomials, eigenvectors properties | PDF unavailable |
| 33 | Similarity | PDF unavailable |
| 34 | Diagonalization | PDF unavailable |
| 35 | Relationship between eigenvalues of BA and AB | PDF unavailable |
| 36 | Eigenvector and principle of biorthogonality | PDF unavailable |
| 37 | Unitary matrices | PDF unavailable |
| 38 | Properties of unitary matrices | PDF unavailable |
| 39 | Unitary equivalence | PDF unavailable |
| 40 | Schur's triangularization theorem | PDF unavailable |
| 41 | Cayley-Hamilton theorem | PDF unavailable |
| 42 | Uses of cayley-hamilton theorem and diagonalizability revisited | PDF unavailable |
| 43 | Normal matrices: Definition and fundamental properties | PDF unavailable |
| 44 | Fundamental properties of normal matrices | PDF unavailable |
| 45 | QR decomposition and canonical forms | PDF unavailable |
| 46 | Jordan canonical form | PDF unavailable |
| 47 | Determining the Jordan form of a matrix | PDF unavailable |
| 48 | Properties of the Jordan canonical form (part 1) | PDF unavailable |
| 49 | Properties of the Jordan canonical form (part 2) | PDF unavailable |
| 50 | Properties of convergent matrices | PDF unavailable |
| 51 | Polynomials and matrices | PDF unavailable |
| 52 | Other canonical forms and factorization of matrices: Gaussian elimination & LU factorization | PDF unavailable |
| 53 | LU decomposition | PDF unavailable |
| 54 | LU decomposition with pivoting | PDF unavailable |
| 55 | Solving pivoted system and LDM decomposition | PDF unavailable |
| 56 | Cholesky decomposition and uses | PDF unavailable |
| 57 | Hermitian and symmetric matrix | PDF unavailable |
| 58 | Properties of hermitian matrices | PDF unavailable |
| 59 | Variational characterization of Eigenvalues: Rayleigh-Ritz theorem | PDF unavailable |
| 60 | Variational characterization of eigenvalues (continued) | PDF unavailable |
| 61 | Courant-Fischer theorem | PDF unavailable |
| 62 | Summary of Rayliegh-Ritz and Courant-Fischer theorems | PDF unavailable |
| 63 | Weyl's theorem | PDF unavailable |
| 64 | Positive semi-definite matrix, monotonicity theorem and interlacing theorems | PDF unavailable |
| 65 | Interlacing theorem I | PDF unavailable |
| 66 | Interlacing theorem II (Converse) | PDF unavailable |
| 67 | Interlacing theorem (Continued) | PDF unavailable |
| 68 | Eigenvalues: Majorization theorem and proof | PDF unavailable |
| 69 | Location and perturbation of Eigenvalues Part1: Dominant diagonal theorem | PDF unavailable |
| 70 | Location and perturbation of Eigenvalues Part2: Gersgorin's theorem | PDF unavailable |
| 71 | Implications of Gersgorin disc theorem, condition of eigenvalues | PDF unavailable |
| 72 | Condition of eigenvalues for diagonalizable matrices | PDF unavailable |
| 73 | Perturbation of eigenvalues Birkhoff's theorem Hoffman - Weilandt theorem | PDF unavailable |
| 74 | Singular value definition and some remarks. | PDF unavailable |
| 75 | Proof of singular value decomposition theorem. | PDF unavailable |
| 76 | Partitioning the SVD | PDF unavailable |
| 77 | Properties of SVD | PDF unavailable |
| 78 | Generalized inverse of matrices | PDF unavailable |
| 79 | Least squares | PDF unavailable |
| 80 | Constrained least squares | PDF unavailable |
| Sl.No | Language | Book link |
|---|---|---|
| 1 | English | Not Available |
| 2 | Bengali | Not Available |
| 3 | Gujarati | Not Available |
| 4 | Hindi | Not Available |
| 5 | Kannada | Not Available |
| 6 | Malayalam | Not Available |
| 7 | Marathi | Not Available |
| 8 | Tamil | Not Available |
| 9 | Telugu | Not Available |