Vectors, Pure and Applied

A General Introduction to Linear Algebra

T. W. Körner (University of Cambridge)

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English

Cambridge University Press
13 December 2012

Mathematics & Sciences; Mathematics; Algebra; Geometry; Algebraic geometry; Algebraic topology

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.

By: T. W. Körner (University of Cambridge)
Imprint: Cambridge University Press
Country of Publication: United Kingdom
Dimensions: Height: 255mm, Width: 173mm, Spine: 24mm
Weight: 830g
ISBN: 9781107675223
ISBN 10: 1107675227
Pages: 452
Publication Date: 13 December 2012
Audience: College/higher education , Professional and scholarly , Primary , Undergraduate
Format: Paperback
Publisher's Status: Active

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.

T. W. Koerner 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.

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

'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