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Numerical Range

The Field of Values of Linear Operators and Matrices

  • Book
  • © 1997

Overview

Authors:
  1. Karl E. Gustafson

    1. Department of Mathematics, University of Colorado at Boulder, Boulder, USA

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    You can also search for this author in PubMed   Google Scholar

  2. Duggirala K. M. Rao

    1. Department of Mathematics, Colegio Bolivar at Cali, Cali, Colombia

    View author publications

    You can also search for this author in PubMed   Google Scholar

Part of the book series: Universitext (UTX)

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Table of contents (6 chapters)

  1. Front Matter

    Pages i-xiv
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  2. Numerical Range

    • Karl E. Gustafson, Duggirala K. M. Rao
    Pages 1-26

  3. Mapping Theorems

    • Karl E. Gustafson, Duggirala K. M. Rao
    Pages 27-48

  4. Operator Trigonometry

    • Karl E. Gustafson, Duggirala K. M. Rao
    Pages 49-79

  5. Numerical Analysis

    • Karl E. Gustafson, Duggirala K. M. Rao
    Pages 80-108

  6. Finite Dimensions

    • Karl E. Gustafson, Duggirala K. M. Rao
    Pages 109-149

  7. Operator Classes

    • Karl E. Gustafson, Duggirala K. M. Rao
    Pages 150-169

  8. Back Matter

    Pages 171-190
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Keywords

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.

Authors and Affiliations

  • Department of Mathematics, University of Colorado at Boulder, Boulder, USA

    Karl E. Gustafson

  • Department of Mathematics, Colegio Bolivar at Cali, Cali, Colombia

    Duggirala K. M. Rao

Bibliographic Information

  • Book Title: Numerical Range

  • Book Subtitle: The Field of Values of Linear Operators and Matrices

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

  • Series Title: Universitext

  • DOI: https://doi.org/10.1007/978-1-4613-8498-4

  • Publisher: Springer New York, NY

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer Science+Business Media New York 1997

  • Softcover ISBN: 978-0-387-94835-5Published: 07 November 1996

  • eBook ISBN: 978-1-4613-8498-4Published: 06 December 2012

  • Series ISSN: 0172-5939

  • Series E-ISSN: 2191-6675

  • Edition Number: 1

  • Number of Pages: XIV, 190

  • Number of Illustrations: 11 illustrations in colour

  • Topics: Analysis

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