LINEAR ALGEBRA
- Course Code
- MA 2506
- Credit Points
- 15
- Course Coordinator
- Dr R Kessar
Pre-requisites
MA 1006 and MA 2004 or, with permission of the Head of Mathematical Sciences, MA 1507 and MA 2004.
Overview
- 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.
Structure
12 week course - 3 one-hour lectures and 1 one-hour tutorial per week (to be arranged).
Assessment
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.