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Universitext

Numerical Range

The Field of Values of Linear Operators and Matrices

Authors: Gustafson, Karl E., Rao, Duggirala K.M.

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About this book

The theories of quadratic forms and their applications appear in many parts of mathematics and the sciences. All students of mathematics have the opportunity to encounter such concepts and applications in their first course in linear algebra. This subject and its extensions to infinite dimen­ sions comprise the theory of the numerical range W(T). There are two competing names for W(T), namely, the numerical range of T and the field of values for T. The former has been favored historically by the func­ tional analysis community, the latter by the matrix analysis community. It is a toss-up to decide which is preferable, and we have finally chosen the former because it is our habit, it is a more efficient expression, and because in recent conferences dedicated to W(T), even the linear algebra commu­ nity has adopted it. Also, one universally refers to the numerical radius, and not to the field of values radius. Originally, Toeplitz and Hausdorff called it the Wertvorrat of a bilinear form, so other good names would be value field or form values. The Russian community has referred to it as the Hausdorff domain. Murnaghan in his early paper first called it the region of the complex plane covered by those values for an n x n matrix T, then the range of values of a Hermitian matrix, then the field of values when he analyzed what he called the sought-for region.

Table of contents (6 chapters)

Buy this book

eBook 67,82 €
price for Spain (gross)
  • ISBN 978-1-4613-8498-4
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover 83,15 €
price for Spain (gross)
  • ISBN 978-0-387-94835-5
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
  • The final prices may differ from the prices shown due to specifics of VAT rules
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Bibliographic Information

Bibliographic Information
Book Title
Numerical Range
Book Subtitle
The Field of Values of Linear Operators and Matrices
Authors
Series Title
Universitext
Copyright
1997
Publisher
Springer-Verlag New York
Copyright Holder
Springer Science+Business Media New York
eBook ISBN
978-1-4613-8498-4
DOI
10.1007/978-1-4613-8498-4
Softcover ISBN
978-0-387-94835-5
Series ISSN
0172-5939
Edition Number
1
Number of Pages
XIV, 190
Number of Illustrations and Tables
11 illustrations in colour
Topics