The Schur Complement and Its Applications

  • Fuzhen Zhang

Part of the Numerical Methods and Algorithms book series (NUAL, volume 4)

Table of contents

  1. Front Matter
    Pages i-xvi
  2. Roger A. Horn, Fuzhen Zhang
    Pages 17-46
  3. Fuzhen Zhang
    Pages 83-110
  4. Charles R. Johnson, Ronald L. Smith
    Pages 111-136
  5. Simo Puntanen, George P. H. Styan
    Pages 163-226
  6. Back Matter
    Pages 259-295

About this book


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.


This book is intended for researchers in linear algebra, matrix analysis, numerical analysis, and statistics.


Eigenvalue Matrix algebra linear algebra numerical analysis

Editors and affiliations

  • Fuzhen Zhang
    • 1
    • 2
  1. 1.Nova Southeastern UniversityFort LauderdaleUSA
  2. 2.Shenyang Normal UniversityShenyangChina

Bibliographic information

  • DOI
  • Copyright Information Springer Science+Business Media, Inc. 2005
  • Publisher Name Springer, Boston, MA
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-0-387-24271-2
  • Online ISBN 978-0-387-24273-6
  • Series Print ISSN 1571-5698
  • Buy this book on publisher's site
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