# 2008/09 Undergraduate Module Catalogue

## MATH2200 Linear Algebra 2

### 10 creditsClass Size: 200

**Module manager:** Dr V. Kisil**Email:** kisilv@maths.leeds.ac.uk

**Taught:** Semester 1 (Sep to Jan) View Timetable

**Year running** 2008/09

### Pre-requisites

MATH1015 | Linear Algebra 1 |

### This module is mutually exclusive with

MATH2080 | Further Linear Algebra |

**This module is approved as an Elective**

### Module summary

This module carries on from Linear Algebra 1 (MATH 1015) and develops the concept of a linear transformation on an abstract vector space. These ideas are then applied to questions about 'changing variables' so as to obtain the simplest form of a matrix or a quadratic form.### Objectives

On completion of this module, students should be able to:a) handle elementary arguments with linear independence, spanning, dimension, and sums of vector spaces over real, complex and finite fields;

b) represent a linear transformation by a matrix with respect to a given basis;

c) determine whether a matrix is diagonalisable and calculate its invariants such as the minimum polynomial;

d) perform standard calculations in real inner product spaces, including the Gram-Schmidt process;

e) diagonalise a quadratic form and determine its rank and signature;

f) show a grasp of the underlying theory by proving the main theorems in the course, and finding other elementary proofs.

### Syllabus

1. Vector spaces, sums of subspaces, over the reals, complexes, or finite fields.

2. Linear transformations and representation of a linear transformation by a matrix. The AP = PB theorem.

3. Diagonalisation of a matrix. Cayley-Hamilton theorem and the minimum polynomial of a matrix. Jordan normal form.

4. Inner product and Euclidean spaces, orthogonal vectors and the Gram-Schmidt process.

5. Quadratic forms and diagonalisation of real and symmetric matrices.

### 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 | 11 | 1.00 | 11.00 |

Lecture | 22 | 1.00 | 22.00 |

Private study hours | 67.00 | ||

Total Contact hours | 33.00 | ||

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

### Reading list

The reading list is available from the Library websiteLast updated: 14/10/2010

## Browse Other Catalogues

- Undergraduate module catalogue
- Taught Postgraduate module catalogue
- Undergraduate programme catalogue
- Taught Postgraduate programme catalogue

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