## Description

Vector spaces, Examples, Linear Dependence, Linear Combinations, Bases and Dimension, Subspaces, Quotient spaces, Direct Sum of vector spaces, Dimension of a direct sum, Dual of a vector space. Matrices and change of basis.

Linear transformation, Algebra of linear transformations, Matrices as linear mappings, Kernal and image, Rank and Nullity theorem, Singular and non-singular linear mappings, Isomorphism, Composition of linear mappings, Polynomials and linear operators, Square matrices as linear operators, matrix representation of a linear operator, Change of basis, characteristic and minimal polynomial for linear operators.