Vectors, Pure and Applied

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

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Description

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.show more

Product details

  • Electronic book text
  • CAMBRIDGE UNIVERSITY PRESS
  • Cambridge University Press (Virtual Publishing)
  • Cambridge, United Kingdom
  • 3 b/w illus. 730 exercises
  • 1139604406
  • 9781139604406

Review quote

'This book will be very useful for mathematics students. Also, mathematics teachers will find many clever ideas to transmit to students.' Julio Benitez, Mathematical Reviewsshow more

About T. W. Korner

T. W. Korner is Professor of Fourier Analysis in the Department of Pure Mathematics and Mathematical Statistics at the University of Cambridge. His previous books include Fourier Analysis and The Pleasures of Counting.show more

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.show more