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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.