Matrix partial orders, shorted operators and applications / Sujit Kumar Mitra, P. Bhimasankaram, Saroj B. Malik.

Format:

Book

Author/Creator:

Mitra, Sujit Kumar.

Contributor:

Bhimasankaram, P.

Malik, Saroj B.

Series:

Series in algebra ; v. 10.

Series in algebra ; v. 10

Language:

English

Subjects (All):

Matrices.

Linear operators.

Physical Description:

1 online resource (464 p.)

Edition:

1st ed.

Place of Publication:

Singapore ; Hackensack, N.J. : World Scientific, c2010.

Language Note:

English

Summary:

The present monograph on matrix partial orders, appearing for the first time, is a unique presentation of many partial orders on matrices that have fascinated mathematicians for their beauty and applied scientists for their wide-ranging application potential. Except for the Lowner order, the partial orders considered are relatively new and came into being in the late 1970's. After a detailed introduction to generalized inverses and decompositions, the three basic partial orders - namely, the minus, the sharp and the star - and the corresponding one-sided orders are presented using various...

Contents:

Preface; Acknowledgements; Glossary of Symbols and Abbreviations; Contents; 1. Introduction; 2. Matrix Decompositions and Generalized Inverses; 3. The Minus Order; 4. The Sharp Order; 5. The Star Order; 6. One-Sided Orders; 7. Unified Theory of Matrix Partial Orders through Generalized Inverses; 8. The L ̈owner Order; 9. Parallel Sums; 10. Schur Complements and Shorted Operators; 11. Shorted Operators - Other Approaches; 12. Lattice Properties of Partial Orders; 13. Partial Orders of Modified Matrices; 14. Equivalence Relations on Generalized and Outer Inverses; 15. Applications

16. Some Open Problems Appendix A Relations and Partial Orders; Bibliography; Index

Notes:

Description based upon print version of record.

Includes bibliographical references and index.

ISBN:

9786612757617

9781282757615

128275761X

9789812838452

9812838457

OCLC:

671654997