Linear Algebra (0590014) 10 credits

This is the version for the year beginning on 1 September of the year

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Aims

To develop the theory of vector spaces over the real and complex fields, by extending the ideas presented in Matrices, Linear Algebra, Geometry module.

Learning Objectives

By the end of the module students are expected:

• to be comfortable with the axiomatic definitions of vector spaces;
• to be able to deduce simple properties of vector spaces from the axioms;
• to be able to determine eigenvalues and eigenvectors of a square matrix;
• to be able to decide whether a given matrix can be diagonalized;
• to understand how linear maps can be represented by matrices;
• to understand the concepts of inner product and inner product space.

• Matrices, Linear Algebra, Geometry (0500007)

1. Characteristic polynomials and Cayley-Hamilton theorem.
2. Abstract vector spaces, linear independence of vectors.
3. Bases in vector spaces, dimension of a vector space.
4. Linear operators and their presentations by matrices.
5. Similar matrices, diagonalization of matrices.
6. Elementary properties of inner product spaces.
7. Gram-Schmidt process.

Recommended Texts:

1. R B J T Allenby, Linear Algebra, Arnold (S 2.897 ALL) *
2. D C Lay, Linear Algebra and its Applications, Addison Wesley (S 2.897 LAY) *

• 2 lectures per week
• weekly seminar

Term taught

Autumn

Assessment

• 1½ hour unseen examination in week 1 Spring Term (90%)
• coursework (10%)

Elective information

Abstract development of the theory of vector spaces.

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Revised 1 September 2003