Linear Algebra

Course Aim

A basic math course for physics and/or engineering students, and also of interest to neuroscientists and others who need linear and matrix algebra in their research. Not intended for those with a solid mathematics degree.

Course Description

A rigorous mathematical introduction to linear algebra, directed at physics or engineering students, but also beneficial to neuroscientists and others who require linear and matrix algebra for research. Course assignments offer practice in working with linear maps between vector spaces, how these can be realized as matrices, and how this can be applied to solving systems of linear equations. Topics include matrix operations, solving systems of linear equations, eigenvalues, eigenvectors, diagonalization and Gram-Schmidt orthonormalization. Not intended for mathematicians.

Course Contents

Fields, vector spaces, and bases.
Matrix operations and solving systems of linear equations.
Row reduction and determinants.
Change of coordinates.
Eigenvalues, eigenvectors, diagonalisation.
Gram-Schmidt orthonormalisation.


Homework 50% – approx. 3 hours per week. There will be 10 homework sets, one each week.
Final exam 50%

Prerequisites or Prior Knowledge

Familiarity with real and complex numbers will be assumed. Ideally, students will have had some previous exposure to mathematical proofs, though this is not strictly required.


Linear Algebra Done Wrong – Sergei Treil


Alternate years course, AY2025

Research Specialties