Module manager: Dr Peter Schuster
Email: pschust@maths.leeds.ac.uk
Taught: Semester 1 (Sep to Jan) View Timetable
Year running 2011/12
| MATH1015 | Linear Algebra 1 |
| MATH2080 | Further Linear Algebra |
This module is approved as an Elective
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.
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.
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.
| Delivery type | Number | Length hours | Student hours |
|---|---|---|---|
| Workshop | 10 | 1 | 10 |
| Lecture | 22 | 1 | 22 |
| Private study hours | 68 | ||
| Total Contact hours | 32 | ||
| Total hours (100hr per 10 credits) | 100 | ||
Regular problem solving assignments
| Assessment type | Notes | % of formal assessment |
|---|---|---|
| In-course Assessment | . | 15 |
| Total percentage (Assessment Coursework) | 15 | |
Normally resits will be assessed by the same methodology as the first attempt, unless otherwise stated
| Exam type | Exam duration | % of formal assessment |
|---|---|---|
| Standard exam (closed essays, MCQs etc) | 2.0 Hrs 0 Mins | 85 |
| Total percentage (Assessment Exams) | 85 | |
Normally resits will be assessed by the same methodology as the first attempt, unless otherwise stated
The reading list is available from the Library website
Last updated: 2/27/2012
Errors, omissions, failed links etc should be notified to the Catalogue Team