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

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Cambridge University Press, 2013 - Mathematics - 444 pages
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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.
  

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Contents

A little geometry
20
The algebra of square matrices
42
The secret life of determinants
60
Abstract vector spaces
87
Linear maps from IF to itself
118
Distance preserving linear maps
160
Diagonalisation for orthonormal bases
192
Cartesian tensors
211
Spaces of linear maps
259
Polynomials in L U U
291
Vector spaces without distances
329
Vector spaces with distances
344
More distances
369
Quadratic forms and their relatives
399
References
438
Copyright

More on tensors
233

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About the author (2013)

T. W. Körner 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.

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