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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, ...