|| MA21410 |
|| LINEAR ALGEBRA |
|| 2007/2008 |
|| Dr Robert J Douglas |
|| Semester 2 |
|| Dr Robert J Douglas |
|| MA11010 |
|| MX31410 |
| Course delivery
|| Seminars / Tutorials || 3 Hours. (3 x 1 hour example classes) |
|| Lecture || 19 Hours. (19 x 1 hour lectures) |
|Assessment Type||Assessment Length/Details||Proportion|
|Semester Exam||2 Hours (written examination) ||100%|
|Supplementary Assessment||2 Hours (written examination) ||100%|
On completion of this module, a student should be able to:
1. determine whether given algebraic structures are vector spaces;
2. apply criteria for subspaces of a vector space;
3. determine bases for vector spaces;
4. prove and apply propositions in the theory of vector spaces;
5. describe the concept of linear transformation;
6. calculate matrices representing linear transformations;
7. determine the rank and nullity of linear transformations and matrices;
8. perform calculations in inner product spaces;
9. diagonalise matrices, especially symmetric matrices.
In this module the concept of a vector space is introduced. This develops some ideas which have occurred in the first year course. It will be seen that superficially different problems in mathematics can be unified. For example, the solution of systems of linear equations and linear diffential equations are essentially the same process and can be dealt with simultaneously in this context.
To develop some matrix theory techniques which have occurred in the first year courses in an abstract setting. To introduce the concepts of a vector space and a mapping between vector spaces. To develop further techniques for computation in vector spaces and to show that this is the correct framework to consider linear problems in a unified way.
1. VECTOR SPACES: Definition and examples, subspaces, spanning sets, linear independence, basis and dimensions.
2. LINEAR TRANSFORMATIONS: Definition and examples, the matrix of a linear transformation, change of basis. The kernel and image of a linear transformation, rank and nullity. The dimension theorem.
3. INNER PRODUCT SPACES: Definition and examples. Orthogonality and Gram-Schmidt orthogonalisation process.
4. DIAGONALISATION OF MATRICES: Eigenvalues and eigenvectors, characteristic equation. Diagonalisation of matrices.
** Recommended Text
Howard Anton & Chris Rorres (2000) Elementary Linear Algebra: Applications Version
8th. J Wiley 0471170526
** Supplementary Text
Allenby, R B J T (1995) Linear Algebra
Edward Arnold 0340610441
Gillett, Ph (1975) Introduction to Linear Algebra
Houghton Mifflin Co. 0395185742
Grossman,S I (1984) Elementary Linear Algebra
2nd. Wadsworth 0534027385
Morris, A O (1982) Linear Algebra - An Introduction
2nd. Chapman and Hall 0412381001
T S Blyth and E F Robertson (1998) Basic Linear Algebra
Whitelaw,T A (1983) An Introduction to Linear Algebra
This module is at CQFW Level 5