| The Schur Complement and Its Applications 2005 Edition Contributor(s): Zhang, Fuzhen (Editor) |
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ISBN: 0387242716 ISBN-13: 9780387242712 Publisher: Springer OUR PRICE: $161.49 Product Type: Hardcover - Other Formats Published: March 2005 Annotation: 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. |
| Additional Information |
| BISAC Categories: - Mathematics | Matrices - Mathematics | Algebra - Linear - Mathematics | Mathematical Analysis |
| Dewey: 512.943 |
| LCCN: 2005042750 |
| Series: Numerical Methods and Algorithms |
| Physical Information: 0.9" H x 9.4" W x 6.3" (1.40 lbs) 312 pages |
| Descriptions, Reviews, Etc. |
| Publisher Description: What's in a name? To paraphrase Shakespeare's Juliet, that which - ilie Haynsworth called the Schur complement, by any other name would be just as beautiful. Nevertheless, her 1968 naming decision in honor of Issai Schur (1875-1941) has gained lasting acceptance by the mathematical com- munity. The Schur complement plays an important role in matrix analysis, statistics, numerical analysis, and many other areas of mathematics and its applications. Our goal is to expose the Schur complement as a rich and basic tool in mathematical research and applications and to discuss many significant re- sults that illustrate its power and fertility. Although our book was originally conceived as a research reference, it will also be useful for graduate and up- per division undergraduate courses in mathematics, applied mathematics, and statistics. The contributing authors have developed an exposition that makes the material accessible to readers with a sound foundation in linear algebra. The eight chapters of the book (Chapters 0-7) cover themes and varia- tions 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 appli- cations in statistics, probability, and numerical analysis. The chapters need not be read in the order presented, and the reader should feel at leisure to browse freely through topics of interest. |