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- About this book
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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.
- Reviews
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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)
- Table of contents (8 chapters)
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Historical Introduction: Issai Schur and the Early Development of the Schur Complement
Pages 1-16
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Basic Properties of the Schur Complement
Pages 17-46
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Eigenvalue and Singular Value Inequalities of Schur Complements
Pages 47-82
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Block Matrix Techniques
Pages 83-110
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Closure Properties
Pages 111-136
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Table of contents (8 chapters)
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Bibliographic Information
- Bibliographic Information
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- Book Title
- The Schur Complement and Its Applications
- Editors
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- Fuzhen Zhang
- Series Title
- Numerical Methods and Algorithms
- Series Volume
- 4
- Copyright
- 2005
- Publisher
- Springer US
- Copyright Holder
- Springer-Verlag US
- eBook ISBN
- 978-0-387-24273-6
- DOI
- 10.1007/b105056
- Hardcover ISBN
- 978-0-387-24271-2
- Softcover ISBN
- 978-1-4419-3712-4
- Series ISSN
- 1571-5698
- Edition Number
- 1
- Number of Pages
- XVI, 295
- Topics
