Applied Linear Algebra (Prof. Andrew Thangaraj, IIT Madras) | Electronics and Electrical Engineering

Applied Linear Algebra

Applied Linear Algebra. Instructor: Prof. Andrew Thangaraj, Department of Electrical Engineering, IIT Madras. This course introduces the fundamentals of vector spaces, inner products, linear transformations, and eigenspaces to electrical engineering students. (from nptel.ac.in)

Introduction

Lecture 01 - Vector Spaces: Introduction

Lecture 02 - Linear Combinations and Span

Lecture 03 - Subspaces, Linear Dependence and Independence

Lecture 04 - Basis and Dimension

Lecture 05 - Sums, Direct Sums and Gaussian Elimination

Lecture 06 - Linear Maps and Matrices

Lecture 07 - Null Space, Range, Fundamental Theorem of Linear Maps

Lecture 08 - Column Space, Null Space and Rank of a Matrix

Lecture 09 - Algebraic Operations on Linear Maps

Lecture 10 - Invertible Maps, Isomorphism, Operators

Lecture 11 - Solving Linear Equations

Lecture 12 - Elementary Row Operations

Lecture 13 - Translates of a Subspace, Quotient Spaces

Lecture 14 - Row Space and Rank of a Matrix

Lecture 15 - Determinants

Lecture 16 - Coordinates and Linear Maps under a Change of Basis

Lecture 17 - Simplifying Matrices of Linear Maps by Choice of Basis

Lecture 18 - Polynomials and Roots

Lecture 19 - Invariant Subspaces, Eigenvalues, Eigenvectors

Lecture 20 - More on Eigenvalues, Eigenvectors, Diagonalization

Lecture 21 - Eigenvalues, Eigenvectors and Upper Triangularization

Lecture 22 - Properties of Eigenvalues

Lecture 23 - Linear State Space Equations and System Stability

Lecture 24 - Discrete-Time Linear Systems and Discrete Fourier Transforms

Lecture 25 - Sequences and Counting Paths in Graphs

Lecture 26 - PageRank Algorithm

Lecture 27 - Dot Product and Length in Cn, Inner Product and Norm in V over F

Lecture 28 - Orthonormal Basis and Gram-Schmidt Orthogonalization

Lecture 29 - Linear Functions, Orthogonal Complements

Lecture 30 - Orthogonal Projection

Lecture 31 - Projection and Distance from a Subspace

Lecture 32 - Linear Equations, Least Squares Solutions and Linear Regression

Lecture 33 - Minimum Mean Squared Error Estimation

Lecture 34 - Adjoint of a Linear Map

Lecture 35 - Properties of Adjoint of a Linear Map

Lecture 36 - Adjoint of an Operator and Operator-Adjoint Product

Lecture 37 - Self-Adjoint Operator

Lecture 38 - Normal Operators

Lecture 39 - Complex Spectral Theorem

Lecture 40 - Real Spectral Theorem

Lecture 41 - Positive Operators

Lecture 42 - Quadratic Forms, Matrix Norms and Optimization

Lecture 43 - Isometries

Lecture 44 - Classification of Operators

Lecture 45 - Singular Values and Vectors of a Linear Map

Lecture 46 - Singular Value Decomposition

Lecture 47 - Polar Decomposition and Some Applications of SVD

References

Applied Linear Algebra
Instructor: Prof. Andrew Thangaraj, Department of Electrical Engineering, IIT Madras. This course introduces the fundamentals of vector spaces, inner products, linear transformations, and eigenspaces to electrical engineering students.