Numerical Range: The Field Of Values Of Linear Operators And Matrices (Universitext) - Brossura

Gustafson, Karl E.

Brossura

ISBN 10: 038794835X ISBN 13: 9780387948355

Casa editrice: Springer, 1996

Riassunto

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 dimensions comprise the theory of the numerical range W(T) This book is dedicated to presenting the fundamentals of the subject. In order to make the book quickly informative, the authors place and keep the subject in a complex Hilbert space. This setting is the heart of the numerical range theory for bounded linear operators T and naturally contains the field of values for finite dimensional matrices T.
This book is a particularly well-prepared account of a beautiful and interesting part of functional analysis that also has important applications in numerical analysis.

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Contenuti

1 Numerical Range.- 1.1 Elliptic Range.- 1.2 Spectral Inclusion.- 1.3 Numerical Radius.- 1.4 Normal Operators.- 1.5 Numerical Boundary.- 1.6 Other W-Ranges.- Endnotes for Chapter 1.- 2 Mapping Theorems.- 2.1 Radius Mapping.- 2.2 Analytic Functions.- 2.3 Rational Functions.- 2.4 Operator Products.- 2.5 Commuting Operators.- 2.6 Dilation Theory.- Endnotes for Chapter 2.- 3 Operator Trigonometry.- 3.1 Operator Angles.- 3.2 Minmax Equality.- 3.3 Operator Deviations.- 3.4 Semigroup Generators.- 3.5 Accretive Products.- 3.6 Antieigenvalue Theory.- Endnotes for Chapter 3.- 4 Numerical Analysis.- 4.1 Optimization Algorithms.- 4.2 Conjugate Gradient.- 4.3 Discrete Stability.- 4.4 Fluid Dynamics.- 4.5 Lax—Wendroff Scheme.- 4.6 Pseudo Eigenvalues.- Endnotes for Chapter 4.- 5 Finite Dimensions.- 5.1 Value Field.- 5.2 Gersgorin Sets.- 5.3 Radius Estimates.- 5.4 Hadamard Product.- 5.5 Generalized Ranges.- 5.6 W(A) Computation.- Endnotes for Chapter 5.- 6 Operator Classes.- 6.1 Resolvent Growth.- 6.2 Three Classes.- 6.3 Spectral Sets.- 6.4 Normality Conditions.- 6.5 Finite Inclusions.- 6.6 Beyond Spectraloid.- Endnotes for Chapter 6.

Dettagli dell'edizione

• Editore: Springer
• Data di pubblicazione: 1996
• Lingua: Inglese
• ISBN 10: 038794835X
• ISBN 13: 9780387948355
• Rilegatura: Copertina flessibile
• Numero di pagine: 208
• Contatto del produttore: ProductSafety@springernature.com; ProductSafety@springernature.com; ; Poststr. 9; Darmstadt; 64293; Germania