Geršgorin and His Circles (Springer Series in Computational Mathematics, 36, Band 36) - Hardcover

Ger¿gorin and His Circles

Buch. Zustand: Neu. Druck auf Anfrage Neuware - Printed after ordering - 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. Artikel-Nr. 9783540211006

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