Linear Algebra

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Linear Algebra provides a valuable introduction to the basic theory of matrices and vector spaces. The book covers: matrices, vector spaces, bases, and dimension; inner products, bilinear and sesquilinear forms over vector spaces; linear transformations, eigenvalues and eigenvectors, diagonalization, and Jordan normal form; and fields and polynomials over fields. Abstract methods are illustrated with concrete examples, and more detailed examples highlight applications of linear algebra to analysis, geometry, differential equations, relativity and quantum mechanics. Rigorous without being unnecessarily abstract, this useful and concise guide to the subject will be important reading for all students in mathematics and related fields.
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Editorial Reviews

From the Publisher

"Kaye offers this work as a second course in linear algebra. As such, it deals with the specific subject matter of linear algebra in a way that could also be viewed as an introduction to abstract algebra or axiomatic mathematics in general. Knowledge of elementary matrix arithmetic and matrix methods--including the general solution to systems of linear equations and computation of inverses and determinants--is assumed, though these topics are briefly reviewed. Some exposure to abstract vector spaces and the notions of basis and dimension would also be helpful to one wishing to peruse this book. For those with a suitable background, this book provides a very rigorous treatment of the fundamentals of linear algebra, including inner product spaces, bilinear and quadratic forms, orthogonal bases, eigenvalues and eigenvectors, and the Jordan canonical form. Certainly appropriate for upper-division undergraduates entertaining thoughts of graduate work in mathematics."--Choice

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Product Details

  • ISBN-13: 9780198502371
  • Publisher: Oxford University Press, USA
  • Publication date: 1/28/1998
  • Series: Oxford Sience Publications
  • Edition description: New Edition
  • Pages: 248
  • Product dimensions: 9.10 (w) x 6.10 (h) x 0.40 (d)

Meet the Author

both at University of Birmingham
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Table of Contents

1 Matrices 3
2 Vector spaces 19
3 Inner product spaces 47
4 Bilinear and sesquilinear forms 61
5 Orthogonal bases 73
6 When is a form definite? 94
7 Quadratic forms and Sylvester's law of inertia 106
8 Linear transformations 127
9 Polynomials 142
10 Eigenvalues and eigenvectors 151
11 The minimum polynomial 162
12 Diagonalization 174
13 Self-adjoint transformations 187
14 The Jordan normal form 203
App. A A theorem of analysis 222
App. B Applications to quantum mechanics 224
Index 227
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