| Gersgorin and His Circles 2004, Corr. 4th Edition Contributor(s): Varga, Richard S. (Author) |
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ISBN: 3540211004 ISBN-13: 9783540211006 Publisher: Springer OUR PRICE: $123.49 Product Type: Hardcover - Other Formats Published: August 2004 Annotation: This book studies the original results, and their extensions, of the Russian mathematician, S.A. Ger?gorin, who wrote a seminal paper in 1931, on how to easily obtain estimates of all n eigenvalues (characteristic values) of any given n-by-n complex matrix. Since the publication of this paper, there has been many newer results spawned by his paper, and this book will be the first which is devoted solely to this resulting area. As such, it will include the latest research results, such as Brauer ovals of Cassini and Brualdi lemniscates, and their comparisons. This book is dedicated to the late Olga Taussky-Todd and her husband, John Todd. It was Olga who brought to light Ger?gorin's paper and its significance to the mathematical world. The level of this book requires only a modest background in linear algebra and analysis, and is therefore comprehensible to upper-level and graduate level students in mathematics. |
| Additional Information |
| BISAC Categories: - Mathematics | Number Systems - Mathematics | Algebra - Elementary - Mathematics | Numerical Analysis |
| Dewey: 512.943 |
| Series: Springer Computational Mathematics |
| Physical Information: 0.72" H x 6.46" W x 9.41" (1.05 lbs) 230 pages |
| Descriptions, Reviews, Etc. |
| Publisher Description: 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. |