School of Computing and Mathematics

Faculty of Natural Sciences

For academic year: 2019/20 Last Updated: 01 March 2020

MAT-30037 - Linear Algebra

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This module introduces the concept of an abstract vector space. The module builds on the knowledge of vectors and matrices gained from first year algebra. Concepts such as linear independence, span and scalar products of vectors are generalised from Euclidean space to other vector spaces, such as function spaces, in such a way that seemingly disparate results from different branches of mathematics are sometimes just different specialisations of the same general concept.

This module will introduce students to abstract vector spaces, which generalise the notions and results of Euclidean space to higher dimensions and vectors which are not sequences of real numbers.

prove theorems on spanning sequences and bases of finite dimensional vector spaces and apply these in concrete and theoretical problems;: 1,2,

find bases for finite dimensional vector spaces and convert vectors into coordinate vectors with respect to a given basis;: 1,2,

recall the definition of a linear transformation and be able to prove and apply the rank-nullity theorem;: 1,2,

recall the definitions of eigenvalue and eigenvector of a linear transformation and apply these concepts to the diagonalisation of square matrices;: 1,2,

define inner products on vector spaces and use these to construct orthonormal bases and orthogonal polynomials.: 1,2,

find bases for finite dimensional vector spaces and convert vectors into coordinate vectors with respect to a given basis;: 1,2,

recall the definition of a linear transformation and be able to prove and apply the rank-nullity theorem;: 1,2,

recall the definitions of eigenvalue and eigenvector of a linear transformation and apply these concepts to the diagonalisation of square matrices;: 1,2,

define inner products on vector spaces and use these to construct orthonormal bases and orthogonal polynomials.: 1,2,

36 hours lectures,

112 hours independent study,

2 hours unseen examination.

112 hours independent study,

2 hours unseen examination.

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Coursework

Continuous assessment will consist of written coursework, problem sheets, class tests or any combination thereof.

2 hour unseen exam

The examination paper will consist of no less than five and not more than eight questions, all of which are compulsory.