Linear Algebra

The details
Mathematical Sciences
Colchester Campus
Undergraduate: Level 5
Thursday 08 October 2020
Friday 18 December 2020
04 February 2021


Requisites for this module


MA204, MA225, MA301, MA316, MA323

Key module for

BSC 5B43 Statistics (Including Year Abroad),
BSC 9K12 Statistics,
BSC 9K13 Statistics (Including Placement Year),
BSC 9K18 Statistics (Including Foundation Year),
BSC G1G4 Mathematics with Computing (Including Year Abroad),
BSC G1G8 Mathematics with Computing (Including Foundation Year),
BSC G1GK Mathematics with Computing,
BSC G1IK Mathematics with Computing (Including Placement Year),
BSC G1F3 Mathematics with Physics,
BSC G1F4 Mathematics with Physics (Including Placement Year),
BSC GCF3 Mathematics with Physics (Including Year Abroad)

Module description

Linear algebra is the branch of abstract algebra studying vectors, vector spaces and maps between them. It provides many useful tools which can be applied throughout mathematics, science, engineering and economics. Linear algebra is so powerful that systems which are linear, or can be approximated as linear, are almost always the easiest to understand and solve. This module introduces the basic definitions and results of the area

Module aims

This module aims to introduce the abstract concepts of vector spaces and linear maps, and show that familiar properties of matrices are special cases of more general results. Fundamental concepts such as basis, dimension, subspace and rank will be introduced and made rigorous.

Module learning outcomes

On completion of the module students should be able to:

- Read and understand advanced abstract mathematical definitions in textbooks and other sources
- Prove simple properties of linear spaces from axioms
- Check whether a set of vectors is a basis
- Check whether a mapping is a linear mapping
- Check whether a linear mapping is onto and whether it is one-to-one
- Find a matrix of a linear mapping
- Change a basis and recalculate the coordinates of vectors and the matrices of mappings

Module information


* Abstract definition and examples of vector spaces
* Subspaces, spans and related results
* Linearly dependent and linearly independent sets and related results
* Bases, dimension and related results
* Linear mappings, the image and the kernel, and related results
* Coordinates of vectors, matrices of linear mappings, change of basis
* The concept of the rank of a matrix and of a linear mapping

Learning and teaching methods

Teaching will be delivered in a way that blends face-to-face classes, for those students that can be present on campus, with a range of online lectures, teaching, learning and collaborative support.


This module does not appear to have any essential texts. To see non-essential items, please refer to the module's reading list.

Assessment items, weightings and deadlines

Coursework / exam Description Deadline Weighting
Coursework   Assignment 1      
Coursework   Assignment 2      
Exam  180 minutes during Summer (Main Period) (Main) 

Overall assessment

Coursework Exam
20% 80%


Coursework Exam
20% 80%
Module supervisor and teaching staff
Dr Alastair Litterick, email:
Dr Alastair Litterick & Dr Jesus Martinez-Garcia
Dr Alastair Litterick (, Dr Jesus Martinez-Garcia (



External examiner

Dr Tania Clare Dunning
The University of Kent
Reader in Applied Mathematics
Prof Stephen Langdon
Brunel University London
Available via Moodle
Of 1332 hours, 0 (0%) hours available to students:
1332 hours not recorded due to service coverage or fault;
0 hours not recorded due to opt-out by lecturer(s).


Further information
Mathematical Sciences

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