| Module Name | Download |
|---|
| Sl.No | Chapter Name | MP4 Download |
|---|---|---|
| 1 | Introduction to the Course | Download |
| 2 | Vector Spaces: Introduction | Download |
| 3 | Linear Combinations and Span | Download |
| 4 | Subspaces, Linear Dependence and Independence | Download |
| 5 | Basis and Dimension | Download |
| 6 | Sums, Direct Sums and Gaussian Elimination | Download |
| 7 | Linear Maps and Matrices | Download |
| 8 | Null space, Range, Fundamental theorem of linear maps | Download |
| 9 | Column space, null space and rank of a matrix | Download |
| 10 | Algebraic operations on linear maps | Download |
| 11 | Invertible maps, Isomorphism, Operators | Download |
| 12 | Solving Linear Equations | Download |
| 13 | Elementary Row Operations | Download |
| 14 | Translates of a subspace, Quotient Spaces | Download |
| 15 | Row space and rank of a matrix | Download |
| 16 | Determinants | Download |
| 17 | Coordinates and linear maps under a change of basis | Download |
| 18 | Simplifying matrices of linear maps by choice of basis | Download |
| 19 | Polynomials and Roots | Download |
| 20 | Invariant subspaces, Eigenvalues, Eigenvectors | Download |
| 21 | More on Eigenvalues, Eigenvectors, Diagonalization | Download |
| 22 | Eigenvalues, Eigenvectors and Upper Triangularization | Download |
| 23 | Properties of Eigenvalues | Download |
| 24 | Linear state space equations and system stability | Download |
| 25 | Discrete-time Linear Systems and Discrete Fourier Transforms | Download |
| 26 | Sequences and counting paths in graphs | Download |
| 27 | PageRank Algorithm | Download |
| 28 | Dot product and length in Cn, Inner product and norm in V over F | Download |
| 29 | Orthonormal basis and Gram-Schmidt orthogonalisation | Download |
| 30 | Linear Functionals, Orthogonal Complements | Download |
| 31 | Orthogonal Projection | Download |
| 32 | Projection and distance from a subspace | Download |
| 33 | Linear equations, Least squares solutions and Linear regression | Download |
| 34 | Minimum Mean Squared Error Estimation | Download |
| 35 | Adjoint of a linear map | Download |
| 36 | Properties of Adjoint of a Linear Map | Download |
| 37 | Adjoint of an Operator and Operator-Adjoint Product | Download |
| 38 | Self-adjoint Operator | Download |
| 39 | Normal Operators | Download |
| 40 | Complex Spectral Theorem | Download |
| 41 | Real Spectral Theorem | Download |
| 42 | Positive Operators | Download |
| 43 | Quadratic Forms, Matrix Norms and Optimization | Download |
| 44 | Isometries | Download |
| 45 | Classification of Operators | Download |
| 46 | Singular Values and Vectors of a Linear Map | Download |
| 47 | Singular Value Decomposition | Download |
| 48 | Polar decomposition and some applications of SVD | Download |
| Sl.No | Chapter Name | English |
|---|---|---|
| 1 | Introduction to the Course | PDF unavailable |
| 2 | Vector Spaces: Introduction | PDF unavailable |
| 3 | Linear Combinations and Span | PDF unavailable |
| 4 | Subspaces, Linear Dependence and Independence | PDF unavailable |
| 5 | Basis and Dimension | PDF unavailable |
| 6 | Sums, Direct Sums and Gaussian Elimination | PDF unavailable |
| 7 | Linear Maps and Matrices | PDF unavailable |
| 8 | Null space, Range, Fundamental theorem of linear maps | PDF unavailable |
| 9 | Column space, null space and rank of a matrix | PDF unavailable |
| 10 | Algebraic operations on linear maps | PDF unavailable |
| 11 | Invertible maps, Isomorphism, Operators | PDF unavailable |
| 12 | Solving Linear Equations | PDF unavailable |
| 13 | Elementary Row Operations | PDF unavailable |
| 14 | Translates of a subspace, Quotient Spaces | PDF unavailable |
| 15 | Row space and rank of a matrix | PDF unavailable |
| 16 | Determinants | PDF unavailable |
| 17 | Coordinates and linear maps under a change of basis | PDF unavailable |
| 18 | Simplifying matrices of linear maps by choice of basis | PDF unavailable |
| 19 | Polynomials and Roots | PDF unavailable |
| 20 | Invariant subspaces, Eigenvalues, Eigenvectors | PDF unavailable |
| 21 | More on Eigenvalues, Eigenvectors, Diagonalization | PDF unavailable |
| 22 | Eigenvalues, Eigenvectors and Upper Triangularization | PDF unavailable |
| 23 | Properties of Eigenvalues | PDF unavailable |
| 24 | Linear state space equations and system stability | PDF unavailable |
| 25 | Discrete-time Linear Systems and Discrete Fourier Transforms | PDF unavailable |
| 26 | Sequences and counting paths in graphs | PDF unavailable |
| 27 | PageRank Algorithm | PDF unavailable |
| 28 | Dot product and length in Cn, Inner product and norm in V over F | PDF unavailable |
| 29 | Orthonormal basis and Gram-Schmidt orthogonalisation | PDF unavailable |
| 30 | Linear Functionals, Orthogonal Complements | PDF unavailable |
| 31 | Orthogonal Projection | PDF unavailable |
| 32 | Projection and distance from a subspace | PDF unavailable |
| 33 | Linear equations, Least squares solutions and Linear regression | PDF unavailable |
| 34 | Minimum Mean Squared Error Estimation | PDF unavailable |
| 35 | Adjoint of a linear map | PDF unavailable |
| 36 | Properties of Adjoint of a Linear Map | PDF unavailable |
| 37 | Adjoint of an Operator and Operator-Adjoint Product | PDF unavailable |
| 38 | Self-adjoint Operator | PDF unavailable |
| 39 | Normal Operators | PDF unavailable |
| 40 | Complex Spectral Theorem | PDF unavailable |
| 41 | Real Spectral Theorem | PDF unavailable |
| 42 | Positive Operators | PDF unavailable |
| 43 | Quadratic Forms, Matrix Norms and Optimization | PDF unavailable |
| 44 | Isometries | PDF unavailable |
| 45 | Classification of Operators | PDF unavailable |
| 46 | Singular Values and Vectors of a Linear Map | PDF unavailable |
| 47 | Singular Value Decomposition | PDF unavailable |
| 48 | Polar decomposition and some applications of SVD | 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 |