# MATU9M4 - Linear Algebra

SCQF Level: 9
Availability: Spring, Advanced module (not Semester 8)
Course Prerequisite: MATU913
Credit Value: 20 (1 module)

### Aims

To provide a grounding in the techniques of linear algebra required for subsequent courses and to provide applications to linear equations, matrices, differential equations, quadratic curves and quadric surfaces.

### Learning Outcomes

Students should be able to identify vector spaces and subspaces, analyze linear transformations, apply criteria for the diagonalizability of a matrix, and carry out calculations in inner product spaces.

### Content

Vector spaces: Homogeneous linear equations, formal definition, subspaces, linear dependence, bases, dimension, intersection and sum of subspaces. Row space, column space, nullspace.
Linear transformations: Simple geometrical transformations of R2 and R3. Basic properties, domain, kernel and range. Matrix representation of linear transformations, co-ordinate vectors, bases for kernel and range.
Diagonalization of matrices: Criteria for diagonalizability, applications, eigenspaces.
Inner-product spaces: Norm, distance, Cauchy-Schwarz inequality and applications, orthogonality, orthonormal bases, orthogonal projections, Gram-Schmidt process, orthogonal diagonalizability of real symmetric matrices, applications.

### Transferable Skills

Ability to abstract essential features of mathematical structures, to think logically and to present clear explanations.

### Bibliography

H. Anton and C Rorres, Elementary Linear Algebra, Applications Version, 9th edn., Wiley, 2005, ISBN: 0-471-449024-4

### Teaching Format

3 one hour lectures and a 1.5 hour tutorial per week.

### Assessment

1/3 coursework (2 class tests) and 2/3 examination.

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