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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