Linear Algebra: Concepts and Methods CONCEPTS AND METHODS

Any student of linear algebra will welcome this textbook, which provides a thorough treatment of this key topic. Blending practice and theory, the book enables the reader to learn and comprehend the standard methods, with an emphasis on understanding how they actually work. At every stage, the authors are careful to ensure that the discussion is no more complicated or abstract than it needs to be, and focuses on the fundamental topics. The book is ideal as a course text or for self-study. Instructors can draw on the many examples and exercises to supplement their own assignments. End-of-chapter sections summarise the material to help students consolidate their learning as they progress through the book.

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.

This thorough, yet concise, textbook covers key topics in first and second-year university courses and includes many examples and exercises with solutions to help students practise and master the relevant methods. Crucially, it fully develops the underlying theory so that students can understand how these methods really work.

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.