MTH2025 · Linear algebra (Advanced)

Overview

Vector spaces, linear transformations. Determinants, eigenvalue problems. Inner products, symmetric matrices, quadratic forms. Linear functionals and dual spaces. Matrix decompositions, least squares approximation, power method. Applications to areas such as coding, economics, networks, graph theory, geometry, dynamical systems, Markov chains, differential equations.

Areas of study: Applied mathematics Financial and insurance mathematics Mathematical statistics Mathematics Pure mathematics

Offerings

Assessment

The Handbook lists an examination for this unit.

Requisites

Learning outcomes

1. Apply concepts related to vector spaces, including subspace, span, linear independence and basis;
2. Understand properties of linear transformations and identify their kernel and range;
3. Diagonalize real matrices by computing their eigenvalues and finding their eigenspaces;
4. Understand matrix decomposition techniques;
5. Understand concepts related to inner product spaces and apply these to problems such as least-squares data fitting;
6. Develop and apply tools from linear algebra to a wide variety of relevant situations;
7. Recognise and apply relevant numerical methods and demonstrate computational skills in linear algebra;
8. Present clear mathematical arguments in both written and oral forms;
9. Develop and present rigorous mathematical proofs.

Workload

• Three 1-hour seminars; • One 2-hour applied class (in weeks 2-12); • One 1-hour workshop and • Six hours of independent study per week.

Student experience, not official rules. Nothing here changes what the Handbook says.