# Unit information: Linear Algebra 2 in 2016/17

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Unit name Linear Algebra 2 MATH21100 20 I/5 Teaching Block 1 (weeks 1 - 12) Dr. Mackay Not open MATH 11005 Linear Algebra & Geometry None School of Mathematics Faculty of Science

## Description

Unit aims

To further develop the theory of vector spaces over arbitrary fields and linear maps between them, including quotient spaces, dual spaces and canonical forms of linear maps. To introduce bilinear and quadratic forms, and to study real and complex vector spaces.

General Description of the Unit

This unit continues the study of vector spaces over arbitrary fields begun in level C/4. The approach taken emphasises building insight and the ability to reason clearly and correctly through careful definitions, and formulation and proof of the key results. The tools and results developed are essential in a variety of areas, both pure and applied, such as geometry, differential equations, group theory and functional analysis.

A major goal is to show that any linear operator on a vector space, even if it is not diagonalisable, can be shown to have a certain canonical form. Another aim is to investigate bilinear and quadratic "forms" over arbitrary fields, and to further develop the study of real and complex inner product spaces.

Relation to Other Units

This unit develops the linear algebra material from first year Linear Algebra & Geometry, giving a general and abstract treatment, using central algebraic structures, such as groups, rings, and fields. This material is an essential part of Pure Mathematics; it is a prerequisite for Representation Theory, and is relevant to other Pure Mathematics units at levels 3 and 4, particularly Functional Analysis.

## Intended learning outcomes

Learning Objectives

Students will deepen their understanding of vector spaces and the natural maps between them. They will be able to state, use and prove fundamental results in linear algebra.sustained argument in a form comprehensible to others.

Transferable Skills

Assimilation of abstract ideas. Reasoning in an abstract context. Setting out a sustained argument in a form comprehensible to others.

## Teaching details

Lectures, problem classes, problems to be done by the students, and solutions to these problems.

## Assessment Details

100% Examination

Raw scores on the examinations will be determined according to the marking scheme written on the examination paper. The marking scheme, indicating the maximum score per question, is a guide to the relative weighting of the questions. Raw scores are moderated as described in the Undergraduate Handbook.

If you fail this unit and are required to resit, reassessment is by a written examination in the August/September Resit and Supplementary exam period.