MA500-1 Mathematics - Advanced Linear Algebra

Semester 1 2017-18

News and Announcements

This module is for students in the course-based M.A. and M.Sc. in Mathematics at NUI Galway, and for research students in the School of Mathematics, Statistics and Applied Mathematics. All interested students are very welcome to participate. Lectures begin on September 4 2017. The Course Outline document is here.

Course Information

Lecturers: Dr Rachel Quinlan, Room ADB-G007, Arás de Brún. Email:
Dr Niall Madden, Room ADB-1013, Arás de Brún. Email:
Lectures: Monday 11:00--11:50 in ADB-1020
Tuesday 12:00--12:50 in ADB-1020
Wednesday 12:00--12:50 in ADB-1020
Course Content This course is an exploration of some topics in linear algebra, from algebraic and algorithmic viewpoints. Linear algebra is a vast subject that pervades virtually all areas of mathematical work including (for example) algebra, analysis, geometry, coding theory, differential equations, numerical analysis, computational mathematics and mathematical modelling. Mostly, we will investigate the spectrum (or list of eigenvalues) of a square matrix. We will consider such questions as why we should care about the spectrum, how to calculate a spectrum, and what can be deduced about the spectrum from structural properties of a matrix or from inspection of its entries. Both theoretical and computational considerations will be included, and we will discuss connections to graph theory and to other areas of mathematics and applied mathematics. The course will include some classical highlights of matrix theory and some of their implications, for example
  • The Cauchy Interlacing Theorem
  • The Perron-Frobenius Theorem
  • The Gershgorin Circle Theorem(s)
  • The Jordan Canonical Form
  • The Singular Value Decomposition.
  • The Schur form
  • The Power method
  • The QR factorisation algorithm.
Assessment: There will be three or four homework assignments during the semester, as well as a single 2-hour exam in the Winter exam session.

Course and Lecture Notes

Outline lecture notes will be posted here in instalments as the module proceeds.

The notes from the versions of this module that were taught by RQ and ran in 15/16 and 16/17 are here and here (but the content changes from year to year).