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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)

Lecture 26 - PageRank Algorithm

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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