London School of Economics and Political Science (LSE)

Modules

Advanced linear algebra [118] (half unit)

Note: this unit cannot be taken with 95 Further mathematics for economists.

Prerequisites (if taken as part of a BSc degree):
05a Mathematics 1 and 05b Mathematics 2.

In Mathematics 2, students have learned about diagonalisation of 2 by 2 matrices, and in Mathematics 1 and 2 students will have learned about solving systems of linear equations. In this course, the theoretical underpinning to these techniques is given, together with some applications, and some new ideas and techniques.

Topics covered are: Vector spaces, linear independence, basis, dimension, linear transformations, similarity, eigenvalues and eigenvectors, diagonalization, systems of difference and differential equations, powers of matrices, Markov chains, inner products, orthogonality, quadratic forms, orthogonal diagonalization, complex matrices, direct sums and projections, least squares, spectral theory, generalized inverses.