# InfoCoBuild

## 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.