Linear Algebra

Paperback | January 1, 1998

byRichard Kaye, Robert Wilson

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This book covers the basic theory of matrices and vector spaces. The book's three main parts cover (I) matrices, vector spaces, bases, and dimension; (II) inner products, bilinear and sesquilinear forms over vector spaces; (III) linear transformations, eigenvalues and eigenvectors,diagonalization, and Jordan normal form. An introduction to fields and polynomials over fields is also provided, and examples and applications are provided throughout. The approach throughout is rigorous, but without being unnecessarily abstract. In particular, this book would be suitable readingfor a student with no prior exposure to abstract algebra. Although intended as a 'second course', the book is completely self-contained and all the material usually given in a 'first course' in presented fully in Part I, so the book provides a useful guide to the entire theory of vector spaces asusually studied in an undergraduate degree. Abstract methods are illustrated with concrete examples throughout, and more detailed examples highlight applications of linear algebra to analysis, geometry, differential equations, relativity and quantum mechanics. As such, the book provides a valuableintroduction to a wide variety of mathematical methods.

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This book covers the basic theory of matrices and vector spaces. The book's three main parts cover (I) matrices, vector spaces, bases, and dimension; (II) inner products, bilinear and sesquilinear forms over vector spaces; (III) linear transformations, eigenvalues and eigenvectors,diagonalization, and Jordan normal form. An introduct...

Richard Kaye is at University of Birmingham. Rob Wilson is at University of Birmingham.

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Format:PaperbackDimensions:242 pages, 9.21 × 6.14 × 0.59 inPublished:January 1, 1998Publisher:Oxford University Press

The following ISBNs are associated with this title:

ISBN - 10:0198502370

ISBN - 13:9780198502371

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Table of Contents

1. Matrices2. Vector spaces3. Inner product spaces4. Bilinear and sesquilinear forms5. Orthogonal bases6. When in a form definite?7. Quadratic forms8. Linear transformations9. Polynomials10. Eigenvalues and eigenvectors11. The minimum polynomial12. Diagonalization13. Self-adjoint transformations14. The Jordan normal form

Editorial Reviews

Clearly and carefully written book that lecturers could easily lecture from and learners readily learn from: it merits a wide circulation.