production
Skip to Content

MA2506: LINEAR ALGEBRA (2014-2015)

Last modified: 28 Jun 2018 10:27


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
Term Second Term Credit Points 15 credits (7.5 ECTS credits)
Campus None. Sustained Study No
Co-ordinators
  • Dr Ellen Henke

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

None.

What other courses must be taken with this course?

None.

What courses cannot be taken with this course?

None.

Are there a limited number of places available?

No

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.

Contact Teaching Time

Information on contact teaching time is available from the course guide.

Teaching Breakdown

More Information about Week Numbers


Details, including assessments, may be subject to change until 30 August 2024 for 1st term courses and 20 December 2024 for 2nd term courses.

Summative Assessments

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.

Feedback

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.

Course Learning Outcomes

None.

Compatibility Mode

We have detected that you are have compatibility mode enabled or are using an old version of Internet Explorer. You either need to switch off compatibility mode for this site or upgrade your browser.