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. 'Linear Algebra: Concepts and Methods is bound to be a very successful book in today's market. I for one intend to use it the next time I'm at bat in the linear algebra line-up.' Michael Berg, MAA Reviews 'The book is written with clear and simple language, accessible for beginners, its contents is well balanced. It is a reader-friendly, fairly interactive and helpful text ... Undoubtedly, this is a fine textbook for the beginners including students in economics, management, finance and social sciences including the ones studying at distance.' Peter Zabreiko, Zentralblatt MATHPreface; 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.