Linear Algebra: 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.

Spis treści:
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.