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MA2506: LINEAR ALGEBRA (2014-2015)

Last modified: 29 Jul 2014 09:33

Course Overview

Linear algebra is the study of vector spaces and linear maps between them.

It provides foundations for almost all branches of mathematics and sciences in general. For example, special relativity and quantum mechanics are formulated within the framework of linear algebra.

Course Details

Study Type Undergraduate Level 2
Session Second Sub Session Credit Points 15 credits (7.5 ECTS credits)
Campus None. Sustained Study No
  • Dr Ellen Henke

Qualification Prerequisites

  • Programme Level 2

What courses & programmes must have been taken before this course?

What other courses must be taken with this course?


What courses cannot be taken with this course?


Are there a limited number of places available?


Course Description

  • Fields. Solving a linear system over a field; Definition and examples of fields (Q, R, C, Fp ); Elementary row operations, row echelon form, Gaussian algorithm for solving a linear system over a field.
  • Vector spaces Definition of a vector space over a field; Examples; subspaces of a vector space, intersection and sum of subspaces; Span, spanning sets; Linear independence; Basis, dimension; Elementary results about bases and dimension; Change of basis matrix.
  • Linear maps Definition of a linear map between two K-vector spaces; Kernel, image, injective, surjective linear maps; Matrix of a linear map; Rank of a matrix; Invertible matrices; Determinants; Change of basis and the matrix of a linear map.
  • Eigenvalues, eigenvectors and diagonalisation Linear transformations, eigenvalues and eigenvectors of linear transformations; elementary properties; Minimal polynomial, characteristic polynomial, Cayley-Hamilton theorem; Triangularisation and diagonalisation.
  • Inner product spaces, Euclidian/Hermitian spaces Basic definitions, examples; Constructing an orthogonal basis using Gram-Schmidt; Symmetric matrices, orthogonal transformations and matrices, unitary transformations and matrices.

Degree Programmes for which this Course is Prescribed

  • BSc Applied Mathematics
  • BSc Mathematics
  • BSc Mathematics & Engineering Mathematics
  • BSc Mathematics with Gaelic
  • MA Applied Mathematics
  • MA Mathematics
  • MA Mathematics with Computing
  • Mathematics Joint
  • Mathematics Major
  • Mathematics Minor

Contact Teaching Time

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Teaching Breakdown


1st Attempt: 1 two-hour written examination (80%); in-course assessment (20%).

Resit: 1 two-hour written examination paper, maximum resit (100%) and resit (80%) with in-course assessment (20%).

Formative Assessment

Informal assessment of weekly homework through discussions in tutorials.


In-course assignments will normally be marked within one week and feedback provided to students in tutorials. Students will be invited to contact the Course Coordinator for feedback on the final examination.

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