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"Contains numerous simple examples and illustrative diagrams....For anyone seeking information about eigenvalue inclusion theorems, this book will be a great reference." --Mathematical Reviews
This book studies the original results, and their extensions, of the Russian mathematician S.A. Geršgorin 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.
- Sales Rank: #5207758 in Books
- Published on: 2010-02-19
- Original language: English
- Number of items: 1
- Dimensions: 9.00" h x .57" w x 6.00" l, .0 pounds
- Binding: Paperback
- 230 pages
Review
From the reviews:
"This book is an extremely detailed account of eigenvalue inclusion theorems, starting with the basic Geršgorin disk theorem … . One of the most pleasing features of the book is what Varga calls the first recurring theme: every eigenvalue inclusion theorem has a corresponding nonsingularity theorem. … contains numerous simple examples and illustrative diagrams, and everything is explained in great detail. … For anyone seeking information about eigenvalue inclusion theorems, this book will be a great reference." (David Scott Watkins, Mathematical Reviews, 2005h)
"The monograph presents a survey of results about spectrum localization for matrices, beginning with the first Geršgorin’s eigenvalue inclusion result … . This book contains many new and some unpublished results as a survey of many Geršgorin type results in the literature. The presented material is almost entirely self-contained with exercises which are useful both for graduate students in mathematics and physicists, engineers and computer scientists." (Boris V. Loginov, Zentralblatt MATH, 1057:8, 2005)
"The new book of Varga contains, along with several new results, nearly all that has been discovered about eiegnvalue inclusions since 1931. … One of the merits of this book is the information that it provides about Semën Aronovic Gersgorin … . I like this book and recommend reading it." (L. Elsner, American Mathematical Monthly, Vol. 113, April, 2006)
Most helpful customer reviews
1 of 1 people found the following review helpful.
Fine scholarly work
By Math Student
This book wraps up a long standing issue in linear algebra regarding how one can estimate the eigenvalues of a complex matrix using elementary row and column sums. For the professional mathematician, this book lays out the important extensions of Gerschgorin's famous estimates in an easily accessible manner.
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