The Schur Complement and Its Applications
Información General
- Autores: Fuzhen Zhang
- Editores: New York : Springer, 2005
- Año de publicación: 2005
- País: Estados Unidos
- Idioma: inglés
- ISBN: 978-0-387-24271-2, 978-0-387-24273-6
- Texto completo no disponible (Saber más ...)
Resumen
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.
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.
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Índice
Preface.- Historical Introduction: Issai Schur and the Early Development of the Schur Complement.- Basic Properties of the Schur Complement.- Eigenvalue and Singular Value Inequalities of Schur Complements.- Block Matrix Techniques.- Closure Properties.- Schur Complements and Matrix Inequalities: Operator-Theoretic Approach.- Schur Complements in Statistics and Probability.- Schur Complements and Applications in Numerical Analysis.- Bibliography.- Notation.- Index.
