Linear Algebra (U01478)

? Credit Points : 10 ? SCQF Level : 8 ? Acronym : MAT-2-LiA

Core second year course for Honours Degrees in Mathematics and/or Statistics.

Syllabus summary: Definition of vector spaces over R and C. Examples. Spans, subspaces, linear independence and bases. Sums and the dimension theorem for subspaces. Change of basis. Linear mappings, the rank theorem, matrices and change of basis, diagonalisation. Inner product spaces. Orthogonality, orthogonal bases, projections. Self-adjointness and diagonalisation of symmetric matrices.

Entry Requirements

? Pre-requisites : Prior attendance at MAT-2-FoC, MAT-2-SVC

? Prohibited combinations : MAT-2-mi3, MAT-2-am3, MAT-2-am3I

Subject Areas

Home subject area

Specialist Mathematics & Statistics (Year 2), (School of Mathematics, Schedule P)

Delivery Information

? Normal year taken : 2nd year

? Delivery Period : Semester 2 (Blocks 3-4)

? Contact Teaching Time : 2 hour(s) 30 minutes per week for 11 weeks

All of the following classes

Type	Day	Start	End	Area
Lecture	Monday	12:10	13:00	KB
Lecture	Wednesday	12:10	13:00	KB

? Additional Class Information : Tutorials: Th at 1110 and 1210.

Summary of Intended Learning Outcomes

1. Understanding of the basic concepts of linear algebra.
2. Computational facility with vectors and matrices: calculation of bases of subspaces, coordinates relative to a basis, matrix of a linear mapping with respect to given bases, etc.
3. Understanding of the notion of an inner product space and the basic concepts therein.
4. Understanding of the adjoint of a linear mapping on an inner product space and of the finite-dimensional spectral theorem.