Lecture 1 - Binary Operation and Groups
Lecture 2 - Vector Spaces
Lecture 3 - Some Examples of Vector Spaces
Lecture 4 - Some Examples of Vector Spaces (Continued...)
Lecture 5 - Subspace of a Vector Space
Lecture 6 - Spanning Set
Lecture 7 - Properties of Subspaces
Lecture 8 - Properties of Subspaces (Continued...)
Lecture 9 - Linearly Independent and Dependent Vectors
Lecture 10 - Linearly Independent and Dependent Vectors (Continued...)
Lecture 11 - Properties of Linearly Independent and Dependent Vectors
Lecture 12 - Properties of Linearly Independent and Dependent Vectors (Continued...)
Lecture 13 - Basis and Dimension of a Vector Space
Lecture 14 - Example of Basis and Standard Basis of a Vector Space
Lecture 15 - Linear Functions
Lecture 16 - Range Space of a Matrix and Row Reduced Echelon Form
Lecture 17 - Row Equivalent Matrices
Lecture 18 - Row Equivalent Matrices (Continued...)
Lecture 19 - Null Space of a Matrix
Lecture 20 - Four Subspaces Associated with a Given Matrix
Lecture 21 - Four Subspaces Associated with a Given Matrix (Continued...)
Lecture 22 - Linear Independence of the rows and columns of a Matrix
Lecture 23 - Application of Diagonal Dominant Matrices
Lecture 24 - Application of Zero Null Space: Interpolating Polynomial and Wronskian Matrix
Lecture 25 - Characterization of basic of a Vector Space and its Subspaces
Lecture 26 - Coordinate of a Vector with respect to Ordered Basis
Lecture 27 - Examples of different subspaces of a vector space of polynomials having degree less than or equal to 3
Lecture 28 - Linear Transformation
Lecture 29 - Properties of Linear Transformation
Lecture 30 - Determining Linear Transformation on a Vector Space by its value on the basis element
Lecture 31 - Range space and null space of a Linear Transformation
Lecture 32 - Rank and Nuility of a Linear Transformation
Lecture 33 - Rank Nuility Theorem
Lecture 34 - Application of Rank Nuility Theorem and Inverse of a Linear Transformation
Lecture 35 - Matrix Associated with Linear Transformation
Lecture 36 - Matrix Representation of a Linear Transformation Relative to Ordered Bases
Lecture 37 - Matrix Representation of a Linear Transformation Relative to Ordered Bases (Continued...)
Lecture 38 - Linear Map Associated with a Matrix
Lecture 39 - Similar Matrices and Diagonalisation of Matrix
Lecture 40 - Orthonormal bases of a Vector Space
Lecture 41 - Gram-Schmidt Orthogonalisation Process
Lecture 42 - QR Factorisation
Lecture 43 - Inner Product Spaces
Lecture 44 - Inner Product of different real vector spaces and basics of complex vector space
Lecture 45 - Inner Product on complex vector spaces and Cauchy-Schwarz inequality
Lecture 46 - Norm of a Vector
Lecture 47 - Matrix Norm
Lecture 48 - Sensitivity Analysis of a System of Linear Equations
Lecture 49 - Orthoganality of the four subspaces associated with a matrix
Lecture 50 - Best Approximation: Least Square Method
Lecture 51 - Best Approximation: Least Square Method (Continued...)
Lecture 52 - Jordan-Canonical Form
Lecture 53 - Some examples on the Jordan form of a given matrix and generalised eigon vectors
Lecture 54 - Singular value decomposition (SVD) theorem
Lecture 55 - Matlab/Octave code for Solving SVD
Lecture 56 - Pseudo-Inverse/Moore-Penrose Inverse
Lecture 57 - Householder Transformation
Lecture 58 - Matlab/Octave code for Householder Transformation
