Lecture 1 : Matrices, System of Linear Equations, Gauss Elimination Method
Lecture 2 : Echelon Form, Elementary Matrices & Row Reduction
Lecture 5 : Determinant, Computation of Inverse & Cramer's Rule
Lecture 7 : Linear Span of vectors, Linearly Independent & Basis Vectors
Lecture 12 : Solvability of System of Linear Equations using Rank
Lecture 13 : Inner Product Space & Cauchy-Schwarz Inequality
Lecture 14 : Orthogonal Basis, Gram Schmidt Orthogonalization & Orthogonal projection
Lecture 15 : Direct Sum of Subspaces, Fundamental Subspaces, Least Square Solutions
Lecture 16 : Eigen Vectors, Eigen Values & Diagonalization of Matrices
Lecture 17 : Diagonalization of Matrices, Examples and applications
Lecture 18 : Orthogonal Matrix and Diagonalization of real symmetric matrices
Lecture 19 : Existence of Basis : Zorn's Lemma