## MATH2080 Further Linear Algebra

### 10 creditsClass Size: 200

Module manager: Professor J.R. Partington
Email: J.R.Partington@leeds.ac.uk

Taught: Semester 1 (Sep to Jan) View Timetable

Year running 2008/09

### Pre-requisite qualifications

MATH1015, or MATH1060, or equivalent.

### This module is mutually exclusive with

 MATH2200 Linear Algebra 2

This module is approved as an Elective

### Module summary

This module is aimed mainly at Joint Honours students. It carries on from Linear Algebra, MATH1060, and develops the more abstract ideas of vector spaces and linear transformations. These ideas are then applied to questions about changing bases, so that the matrices become as simple as possible.

### Objectives

To introduce the idea of linear transformation and some of its applications, and to develop sufficient theory, e.g. diagonalisation, for applications in Pure and Applied Mathematics and Statistics. On completion of this module, students should be able to reproduce the appropriate definitions accurately, reproduce short proofs that they have seen in the module and do examples on the material which are more challenging than those at level 1.

### Syllabus

1. Revision of vector spaces and subspaces, including axioms for vector spaces over the real numbers, the complex numbers and the field of two elements. Revision of linear dependence and independence. 1. Spanning sets and bases. 2. Definition of a linear transformation, image and kernel of a linear transformation. 3. Linear transformations and matrices: By taking bases of V and W, a linear transformation from V to W corresponds to a matrix. Equivalence, canonical form under equivalence. Isomorphism. 4. Case when V=W: similarity.
5. For vector spaces over R or C, revision of eigenvalues, eigenvectors, characteristic equation. Jordan canonical form, Cayley Hamilton Theorem, Minimum polynomial.

### Teaching methods

Due to COVID-19, teaching and assessment activities are being kept under review - see module enrolment pages for information

 Delivery type Number Length hours Student hours Example Class 10 1.00 10.00 Lecture 22 1.00 22.00 Private study hours 68.00 Total Contact hours 32.00 Total hours (100hr per 10 credits) 100.00

### Methods of assessment

Due to COVID-19, teaching and assessment activities are being kept under review - see module enrolment pages for information

Coursework
 Assessment type Notes % of formal assessment In-course Assessment . 15.00 Total percentage (Assessment Coursework) 15.00

Normally resits will be assessed by the same methodology as the first attempt, unless otherwise stated

Exams
 Exam type Exam duration % of formal assessment Standard exam (closed essays, MCQs etc) 2 hr 00 mins 85.00 Total percentage (Assessment Exams) 85.00

Normally resits will be assessed by the same methodology as the first attempt, unless otherwise stated