Introduction, Vector spaces, Subspaces, Linear Combinations, Linear Spans, row space and column space of a Matrix, Linear Dependence and Independence, Basis and Dimension, Coordinates.

(RBT Levels: L1, L2 and L3)

Teaching-Learning Process: Chalk and talk method / PowerPoint Presentation

Introduction, Linear Mappings, Geometric linear transformation of i2, Kernel and Image of a linear transformations, Rank-Nullity Theorem (No proof), Matrix representation of linear transformations, Singular and Non-singular linear transformations, Invertible linear transformations

(RBT Levels: L1, L2 and L3)

Teaching-Learning Process: Chalk and talk method / PowerPoint Presentation

Introduction, Polynomials of Matrices, Applications of Cayley-Hamilton Theorem, Eigen spaces of a linear transformation, Characteristic and Minimal Polynomials of Block Matrices, Jordan Canonical form.

(RBT Levels: L1, L2 and L3)

Teaching-Learning Process: Chalk and talk method / PowerPoint Presentation

Inner products, inner product spaces, length and orthogonality, orthogonal sets and Bases, projections, Gram-Schmidt process, QR-factorization, least squares problem and least square error.

(RBT Levels: L1, L2 and L3)

Teaching-Learning Process: Chalk and talk method / PowerPoint Presentation

Diagonalization and Orthogonal diagonalization of real symmetric matrices, quadratic forms and its classifications, Hessian Matrix, Method of steepest descent, Singular value decomposition. Dimensionality reduction – Principal component analysis.

(RBT Levels: L1, L2 and L3)

Teaching-Learning Process: Chalk and talk method / PowerPoint Presentation