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This book describes the Schur complement as a rich and basic tool in mathematical research and applications and discusses many significant results that illustrate its power and fertility. Coverage includes historical development, basic properties, eigenvalue and singular value inequalities, matrix inequalities in both finite and infinite dimensional settings, closure properties, and applications in statistics, probability, and numerical analysis.
- Sales Rank: #4254767 in Books
- Published on: 2005-03-04
- Original language: English
- Number of items: 1
- Dimensions: 6.30" h x .90" w x 9.40" l, 1.40 pounds
- Binding: Hardcover
- 295 pages
Review
From the reviews of the first edition:
"The book consists of eight chapters, each written by experts in their field, devoted to certain aspects and applications of the Schur complement. They can be read independently of each other. … The book can serve as a research reference, as it contains many new results and results not yet appeared in books. The articles contain thorough expositions, so they can be understood by anyone having a good knowledge of linear algebra." (Ludwig Elsner, Zentralblatt MATH, Vol. 1075, 2006)
From the Back Cover
The Schur complement plays an important role in matrix analysis, statistics, numerical analysis, and many other areas of mathematics and its applications. This book describes the Schur complement as a rich and basic tool in mathematical research and applications and discusses many significant results that illustrate its power and fertility. The eight chapters of the book cover themes and variations on the Schur complement, including its historical development, basic properties, eigenvalue and singular value inequalities, matrix inequalities in both finite and infinite dimensional settings, closure properties, and applications in statistics, probability, and numerical analysis. The chapters need not be read in order, and the reader should feel free to browse freely through topics of interest.
Although the book is primarily intended to serve as a research reference, it will also be useful for graduate and advanced undergraduate courses in mathematics, applied mathematics, and statistics. The contributing authors’ exposition makes most of the material accessible to readers with a sound foundation in linear algebra.
The book, edited by Fuzhen Zhang, was written by several distinguished mathematicians: T. Ando (Hokkaido University, Japan), C. Brezinski (Université des Sciences et Technologies de Lille, France), R. Horn (University of Utah, Salt Lake City, U.S.A.), C. Johnson (College of William and Mary, Williamsburg, U.S.A.), J.-Z. Liu (Xiangtang University, China), S. Puntanen (University of Tampere, Finland), R. Smith (University of Tennessee, Chattanooga, USA), and G.P.H. Steyn (McGill University, Canada). Fuzhen Zhang is a professor of Nova Southeastern University, Fort Lauderdale, U.S.A., and a guest professor of Shenyang Normal University, Shenyang, China.
Audience
This book is intended for researchers in linear algebra, matrix analysis, numerical analysis, and statistics.
Most helpful customer reviews
2 of 2 people found the following review helpful.
Uneven exposition levels but very good overall
By Disappointed
A comprehensive exposition of the title subject. The historical introduction (Chapter 0) is a gem. Chapters are written by different contributors, but with a few exceptions the overall organization is coherent. One minor problem is the disparity of notations for matrix algebra used by contributors. Main missing topic: applications in high performance computing. Exhaustive bibliography.
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