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 )

Lecture 12 - Elementary Row Operations
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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