NPTEL : NOC:Applied Linear Algebra (Electrical Engineering)

Co-ordinators : Prof. Andrew Thangaraj


Lecture 1 - Introduction to the Course

Lecture 2 - Vector Spaces: Introduction

Lecture 3 - Linear Combinations and Span

Lecture 4 - Subspaces, Linear Dependence and Independence

Lecture 5 - Basis and Dimension

Lecture 6 - Sums, Direct Sums and Gaussian Elimination

Lecture 7 - Linear Maps and Matrices

Lecture 8 - Null space, Range, Fundamental theorem of linear maps

Lecture 9 - Column space, null space and rank of a matrix

Lecture 10 - Algebraic operations on linear maps

Lecture 11 - Invertible maps, Isomorphism, Operators

Lecture 12 - Solving Linear Equations

Lecture 13 - Elementary Row Operations

Lecture 14 - Translates of a subspace, Quotient Spaces

Lecture 15 - Row space and rank of a matrix

Lecture 16 - Determinants

Lecture 17 - Coordinates and linear maps under a change of basis

Lecture 18 - Simplifying matrices of linear maps by choice of basis

Lecture 19 - Polynomials and Roots

Lecture 20 - Invariant subspaces, Eigenvalues, Eigenvectors

Lecture 21 - More on Eigenvalues, Eigenvectors, Diagonalization

Lecture 22 - Eigenvalues, Eigenvectors and Upper Triangularization

Lecture 23 - Properties of Eigenvalues

Lecture 24 - Linear state space equations and system stability

Lecture 25 - Discrete-time Linear Systems and Discrete Fourier Transforms

Lecture 26 - Sequences and counting paths in graphs

Lecture 27 - PageRank Algorithm

Lecture 28 - Dot product and length in Cn, Inner product and norm in V over F

Lecture 29 - Orthonormal basis and Gram-Schmidt orthogonalisation

Lecture 30 - Linear Functionals, Orthogonal Complements

Lecture 31 - Orthogonal Projection

Lecture 32 - Projection and distance from a subspace

Lecture 33 - Linear equations, Least squares solutions and Linear regression

Lecture 34 - Minimum Mean Squared Error Estimation

Lecture 35 - Adjoint of a linear map

Lecture 36 - Properties of Adjoint of a Linear Map

Lecture 37 - Adjoint of an Operator and Operator-Adjoint Product

Lecture 38 - Self-adjoint Operator

Lecture 39 - Normal Operators

Lecture 40 - Complex Spectral Theorem

Lecture 41 - Real Spectral Theorem

Lecture 42 - Positive Operators

Lecture 43 - Quadratic Forms, Matrix Norms and Optimization

Lecture 44 - Isometries

Lecture 45 - Classification of Operators

Lecture 46 - Singular Values and Vectors of a Linear Map

Lecture 47 - Singular Value Decomposition

Lecture 48 - Polar decomposition and some applications of SVD