Schur Complement 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. 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.

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.