Vectors, Pure and Applied
Vectors, Pure and Applied
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.
- Shows vectors from many different points of view so that students develop a deeper understanding
- Prepares students for further work in abstract algebra, analysis and physics
- With over 700 exercises, provides ample material for self study
Reviews & endorsements
"This book will be very useful for mathematics students. Also, mathematics teachers will find many clever ideas to transmit to students.
Julio Benitez, Mathematical Reviews
"... an excellent book for mathematically mature students. Recommended."
D.M. Ha, Ryerson University for Choice Magazine
Product details
January 2013Paperback
9781107675223
452 pages
255 × 173 × 24 mm
0.83kg
3 b/w illus. 730 exercises
Available
Table of Contents
- 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.
