# 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)

 Lecture 19 - Invariant Subspaces, Eigenvalues, Eigenvectors

Go to the Course Home or watch other lectures:

 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