# InfoCoBuild

## Advanced Matrix Theory and Linear Algebra for Engineers

Advanced Matrix Theory and Linear Algebra for Engineers. Instructor: Prof. Vittal Rao, Centre for Electronics Design and Technology, IISc Bangalore. Introduction to systems of linear equations, Vector spaces, Solutions of linear systems, Important subspaces associated with a matrix, Orthogonality, Eigenvalues and eigenvectors, Diagonalizable matrices, Hermitian and symmetric matrices, General matrices. (from nptel.ac.in)

 Prologue

 Prologue Lecture 01 - Prologue Part 1: Systems of Linear Equations, Matrix Notation Lecture 02 - Prologue Part 2: Diagonalization of a Square Matrix Lecture 03 - Prologue Part 3: Homogeneous Systems, Elementary Row Operations Linear Systems Lecture 04 - Linear Systems 1: Elementary Row Operations (EROs) Lecture 05 - Linear Systems 2: Row Reduced Echelon Form, The Reduction Process Lecture 06 - Linear Systems 3: The Reduction Process, Solution using EROs Lecture 07 - Linear Systems 4: Solution using EROs: Non-homogeneous Systems Vector Spaces Lecture 08 - Vector Spaces Part 1 Lecture 09 - Vector Spaces Part 2 Linear Independence and Subspaces Lecture 10 - Linear Combination, Linear Independence and Dependence Lecture 11 - Linear Independence and Dependence, Subspaces Lecture 12 - Subspace Spanned by a Finite Set of Vectors, The Basic Subspaces Associated with a Matrix Lecture 13 - Subspace Spanned by an Infinite Set of Vectors, Linear Independence of an Infinite Set of Vectors Basis Lecture 14 - Basis, Basis as a Maximal Linearly Independent Set Lecture 15 - Finite Dimensional Vector Spaces Lecture 16 - Extension of a Linearly Independent Set to a Basis, Ordered Basis Linear Transformations Lecture 17 - Relation between Representation in Two Bases, Linear Transformations Lecture 18 - Examples of Linear Transformations Lecture 19 - Null Space and Range of a Linear Transformation Lecture 20 - Rank Nullity Theorem, One-One Linear Transformation Lecture 21 - One-One Linear Transformation, Onto Linear Transformations, Isomorphisms Inner Product and Orthogonality Lecture 22 - Inner Product and Orthogonality Lecture 23 - Orthonormal Sets, Orthonormal Basis and Fourier Expansion Lecture 24 - Fourier Expansion, Gram-Schmidt Orthonormalization, Orthogonal Complements Lecture 25 - Orthogonal Complements, Decomposition of a Vector, Pythagoras Theorem Lecture 26 - Orthogonal Complements in the context of Subspaces Associated with a Matrix Lecture 27 - Best Approximation Diagonalization Lecture 28 - Diagonalization, Eigenvalues and Eigenvectors Lecture 29 - Eigenvalues and Eigenvectors, Characteristic Polynomial Lecture 30 - Algebraic Multiplicity, Eigenvectors, Eigenspaces and Geometric Multiplicity Lecture 31 - Criterion for Diagonalization Hermitian and Symmetric Matrices Lecture 32 - Hermitian and Symmetric Matrices, Unitary Matrix Lecture 33 - Unitary and Orthogonal Matrices, Eigen Properties of Hermitian Matrices, Unitary Diagonalization Lecture 34 - Spectral Decomposition Lecture 35 - Positive and Negative Definite and Semidefinite Matrices Singular Value Decomposition (SVD) Lecture 36 - Singular Value Decomposition (SVD) Part 1 Lecture 37 - Singular Value Decomposition (SVD) Part 2 Back to Linear Systems Lecture 38 - Back to Linear Systems Part 1 Lecture 39 - Back to Linear Systems Part 2 Epilogue Lecture 40 - Epilogue

 References Advanced Matrix Theory and Linear Algebra for Engineers Instructor: Prof. Vittal Rao, Centre for Electronics Design and Technology, IISc Bangalore. Introduction to systems of linear equations, Vector spaces, Solutions of linear systems, ...