Dr James Ward

This course is compulsory on the BSc in Data Science. This course is available as an outside option to students on other programmes where regulations permit. This course is available with permission to General Course students.

Students should ideally have taken the course Mathematical Methods (MA100) or equivalent, entailing intermediate-level knowledge of linear algebra, linear independence, eigenvalues and diagonalisation.

This course develops ideas first presented in MA100. It consists of the linear algebra part of MA212, covering the following topics: Vector spaces and dimension. Linear transformations, kernel and image. Real inner products. Orthogonal matrices, and the transformations they represent. Complex matrices, diagonalisation, special types of matrix and their properties. Jordan normal form, with applications to the solutions of differential and difference equations. Singular values, and the singular values decomposition. Direct sums, orthogonal projections, least square approximations, Fourier series. Right and left inverses and generalized inverses.

This course is delivered through a combination of classes and lectures totalling a minimum of 30 hours in the Lent Term. 

Written answers to set problems will be expected on a weekly basis.

The following is a useful background text: 

• Martin Anthony and Michele Harvey, Linear Algebra: Concepts and Methods (Cambridge University Press 2012).

Exam (100%, duration: 1 hour and 30 minutes) in the summer exam period.