Linear Algebra: Concepts and Methods

Martin Anthony is Professor of Mathematics at the London School of Economics (LSE) and Academic Co-ordinator for Mathematics on the University of London International Programmes for which LSE has academic oversight. He has over 20 years' experience of teaching students at all levels of university and is the author of four books, including the textbook Mathematics for Economics and Finance: Methods and Modelling (Cambridge University Press, 1996). He also has extensive experience of preparing distance learning materials. Michele Harvey currently lectures at the London School of Economics, where she has taught linear algebra as part of the first year mathematical methods course for over 20 years, as the course evolved from about 100 students to over 600. She has been praised for her teaching in student surveys and the student newspaper. She is also Chief Examiner for the Advanced Linear Algebra course on the University of London International Programmes and has co-authored with Martin Anthony the study guides for advanced linear algebra and linear algebra on this programme. She has over 40 years' experience of teaching students at various levels of university in London and in New York.

Preface; Preliminaries: before we begin; 1. Matrices and vectors; 2. Systems of linear equations; 3. Matrix inversion and determinants; 4. Rank, range and linear equations; 5. Vector spaces; 6. Linear independence, bases and dimension; 7. Linear transformations and change of basis; 8. Diagonalisation; 9. Applications of diagonalisation; 10. Inner products and orthogonality; 11. Orthogonal diagonalisation and its applications; 12. Direct sums and projections; 13. Complex matrices and vector spaces; 14. Comments on exercises; Index.