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Ger¿gorin and His Circles
Buch von Richard S Varga
Sprache: Englisch

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Beschreibung
TheGer? sgorin CircleTheorem, averywell-known resultin linear algebra today, stems from the paper of S. Ger? sgorin in 1931 (which is reproduced in AppendixD)where,givenanarbitraryn×ncomplexmatrix,easyarithmetic operationsontheentriesofthematrixproducendisks,inthecomplexplane, whose union contains all eigenvalues of the given matrix. The beauty and simplicity of Ger? sgorin¿s Theorem has undoubtedly inspired further research in this area, resulting in hundreds of papers in which the name ¿Ger? sgorin¿ appears. The goal of this book is to give a careful and up-to-date treatment of various aspects of this topic. The author ?rst learned of Ger? sgorin¿s results from friendly conversations with Olga Taussky-Todd and John Todd, which inspired me to work in this area.Olgawasclearlypassionateaboutlinearalgebraandmatrixtheory,and her path-?nding results in these areas were like a magnet to many, including this author! It is the author¿s hope that the results, presented here on topics related to Ger? sgorin¿s Theorem, will be of interest to many. This book is a?ectionately dedicated to my mentors, Olga Taussky-Todd and John Todd. There are two main recurring themes which the reader will see in this book. The ?rst recurring theme is that a nonsingularity theorem for a mat- ces gives rise to an equivalent eigenvalue inclusion set in the complex plane for matrices, and conversely. Though common knowledge today, this was not widely recognized until many years after Ger? sgorin¿s paper appeared. That these two items, nonsingularity theorems and eigenvalue inclusion sets, go hand-in-hand, will be often seen in this book.
TheGer? sgorin CircleTheorem, averywell-known resultin linear algebra today, stems from the paper of S. Ger? sgorin in 1931 (which is reproduced in AppendixD)where,givenanarbitraryn×ncomplexmatrix,easyarithmetic operationsontheentriesofthematrixproducendisks,inthecomplexplane, whose union contains all eigenvalues of the given matrix. The beauty and simplicity of Ger? sgorin¿s Theorem has undoubtedly inspired further research in this area, resulting in hundreds of papers in which the name ¿Ger? sgorin¿ appears. The goal of this book is to give a careful and up-to-date treatment of various aspects of this topic. The author ?rst learned of Ger? sgorin¿s results from friendly conversations with Olga Taussky-Todd and John Todd, which inspired me to work in this area.Olgawasclearlypassionateaboutlinearalgebraandmatrixtheory,and her path-?nding results in these areas were like a magnet to many, including this author! It is the author¿s hope that the results, presented here on topics related to Ger? sgorin¿s Theorem, will be of interest to many. This book is a?ectionately dedicated to my mentors, Olga Taussky-Todd and John Todd. There are two main recurring themes which the reader will see in this book. The ?rst recurring theme is that a nonsingularity theorem for a mat- ces gives rise to an equivalent eigenvalue inclusion set in the complex plane for matrices, and conversely. Though common knowledge today, this was not widely recognized until many years after Ger? sgorin¿s paper appeared. That these two items, nonsingularity theorems and eigenvalue inclusion sets, go hand-in-hand, will be often seen in this book.
Zusammenfassung

Includes supplementary material: [...]

Inhaltsverzeichnis
Basic Theory.- Geršgorin-Type Eigenvalue Inclusion Theorems.- More Eigenvalue Inclusion Results.- Minimal Geršgorin Sets and Their Sharpness.- G-Functions.- Geršgorin-Type Theorems for Partitioned Matrices.
Details
Erscheinungsjahr: 2004
Fachbereich: Analysis
Genre: Mathematik, Medizin, Naturwissenschaften, Technik
Rubrik: Naturwissenschaften & Technik
Medium: Buch
Reihe: Springer Series in Computational Mathematics
Inhalt: x
230 S.
1 farbige Illustr.
230 p. 1 illus. in color.
ISBN-13: 9783540211006
ISBN-10: 3540211004
Sprache: Englisch
Ausstattung / Beilage: HC runder Rücken kaschiert
Einband: Gebunden
Autor: Varga, Richard S
Hersteller: Springer-Verlag GmbH
Springer Berlin Heidelberg
Springer Series in Computational Mathematics
Verantwortliche Person für die EU: Books on Demand GmbH, In de Tarpen 42, D-22848 Norderstedt, info@bod.de
Maße: 241 x 160 x 20 mm
Von/Mit: Richard S Varga
Erscheinungsdatum: 11.08.2004
Gewicht: 0,567 kg
Artikel-ID: 102472077
Zusammenfassung

Includes supplementary material: [...]

Inhaltsverzeichnis
Basic Theory.- Geršgorin-Type Eigenvalue Inclusion Theorems.- More Eigenvalue Inclusion Results.- Minimal Geršgorin Sets and Their Sharpness.- G-Functions.- Geršgorin-Type Theorems for Partitioned Matrices.
Details
Erscheinungsjahr: 2004
Fachbereich: Analysis
Genre: Mathematik, Medizin, Naturwissenschaften, Technik
Rubrik: Naturwissenschaften & Technik
Medium: Buch
Reihe: Springer Series in Computational Mathematics
Inhalt: x
230 S.
1 farbige Illustr.
230 p. 1 illus. in color.
ISBN-13: 9783540211006
ISBN-10: 3540211004
Sprache: Englisch
Ausstattung / Beilage: HC runder Rücken kaschiert
Einband: Gebunden
Autor: Varga, Richard S
Hersteller: Springer-Verlag GmbH
Springer Berlin Heidelberg
Springer Series in Computational Mathematics
Verantwortliche Person für die EU: Books on Demand GmbH, In de Tarpen 42, D-22848 Norderstedt, info@bod.de
Maße: 241 x 160 x 20 mm
Von/Mit: Richard S Varga
Erscheinungsdatum: 11.08.2004
Gewicht: 0,567 kg
Artikel-ID: 102472077
Sicherheitshinweis