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Vectors, Pure and Applied


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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.

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Explains both the how and the why of linear algebra to get students thinking like mathematicians.

About the Author

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.


'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

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