Matrices and quadratic forms

✍ Scribed by Bowers J.

• Publisher: Butterworth
• Year: 2000
• Tongue: English
• Leaves: 189
• Category: Library

✦ Synopsis

As a basis of equation and problem-solving, linear algebra is the most widely taught sub-division of pure mathematics. Building on both skills and knowledge attained during A-level and earlier degree modules in linear algebra, "Matrices and Quadratic Forms" provides a lively and accessible introduction to matrices and quadratic forms. Examples and exercises are used as teaching aids throughout and ideas for investigation and project work help to place the subject in context. Student motivation and learning is encouraged by the inclusion of historical contexts, real-life situations and the discussion of links with other areas of mathematics. Providing a concise and thorough introduction to matrices and quadratic forms, this is an essential purchase for all students of mathematics. Ideal second text in linear algebra, this book follows on from Allenby's Linear Algebra.Concise and affordable.Written in a straightforward and accessible style by an authority in the field.

✦ Table of Contents

Cover......Page 1
Title......Page 3
Contents......Page 6
Series preface......Page 8
Preface......Page 10
1. Questions about Matrices and Quadratic Forms......Page 12
2. Partitioned Matrices......Page 20
3. Vector Spaces......Page 28
4. Linear Transformations......Page 42
5. The Matrix Representation of Linear Transformations......Page 61
6. Similar Matrices......Page 73
7. Diagonalizable Matrices......Page 26
8. The Cayley-Hamilton Theorem......Page 97
9. The Minimum Polynomial......Page 108
10. Euclidean Vector Spaces......Page 119
11. Orthogonal Matrices......Page 131
12. Quadratic Forms and Symmetric Matrices......Page 140
13. Positive Definite Quadratic Forms......Page 154
14. Further Developments......Page 169
Index......Page 184