Vectors, Pure and Applied: A General Introduction to Linear Algebra [Hardcover]

Explains both the how and the why of linear algebra to get students thinking like mathematicians.Whilst many books in linear algebra focus purely on getting students through exams, this text explains both the how and the why of linear algebra, preparing students for further work in abstract algebra, analysis or physics. Its numerous exercises include questions to challenge even the most able student.Whilst many books in linear algebra focus purely on getting students through exams, this text explains both the how and the why of linear algebra, preparing students for further work in abstract algebra, analysis or physics. Its numerous exercises include questions to challenge even the most able student.Many books in linear algebra focus purely on getting students through exams, but this text explains both the how and the why of linear algebra and enables students to begin thinking like mathematicians. The author demonstrates how different topics (geometry, abstract algebra, numerical analysis, physics) make use of vectors in different ways and how these ways are connected, preparing students for further work in these areas. The book is packed with hundreds of exercises ranging from the routine to the challenging. Sketch solutions of the easier exercises are available online.Introduction; Part I. Familiar Vector Spaces: 1. Gaussian elimination; 2. A little geometry; 3. The algebra of square matrices; 4. The secret life of determinants; 5. Abstract vector spaces; 6. Linear maps from Fn to itself; 7. Distance preserving linear maps; 8. Diagonalisation for orthonormal bases; 9. Cartesian tensors; 10. More on tensors; Part II. General Vector Spaces: 11. Spaces of linear maps; 12. Polynomials in L(U,U); 13. Vector spaces without distances; 14. Vector spaces with distances; 15. More distances; 16. Quadratic forms and their relatives; Bibliography; Index. This book will be very useful for mathematics students. Also, mathematics teachers will find many clever ideas to transmit l“œ