electiveHQ

This module gives an introduction to the theory of (finite-dimensional) vector spaces over fields and linear transformations (i.e., the functions between vector spaces that preserve the vector space structure). The module relies on the theory of systems of linear equations and matrix algebra, developed in first year. The main topics are as follows: brief revision of Gaussian elimination and Gauss-Jordan elimination, vector spaces over a field, subspaces, spanning sets, linear independence, bases, dimension, coordinate spaces, matrix techniques, row space, column space, null space, rank and nullity of a matrix, eigenvalues, eigenvectors, diagonalization, revision of functions on sets and their properties, linear transformations, kernel and image, isomorphisms, matrix of a linear transformation, vector space of linear transformations, change of bases for matrices of linear transformations, rank and nullity of a linear transformation, quotient spaces, dimension formula, first isomorphism theorem, rank-nullity theorem. [Disclaimer: module content and assessment strategies may be subject to minor changes during the trimester. These changes may not be reflected in this module descriptor at that time, but will be clearly communicated to all students via other means.]