03167nam 2200637 a 450 991078088140332120230725041540.01-282-75761-X9786612757617981-283-845-7(CKB)2490000000001864(EBL)731077(OCoLC)671654997(SSID)ssj0000422831(PQKBManifestationID)12209492(PQKBTitleCode)TC0000422831(PQKBWorkID)10432624(PQKB)10551664(MiAaPQ)EBC731077(WSP)00007170(Au-PeEL)EBL731077(CaPaEBR)ebr10422474(CaONFJC)MIL275761(EXLCZ)99249000000000186420100823d2010 uy 0engurcn|||||||||txtccrMatrix partial orders, shorted operators and applications[electronic resource] /Sujit Kumar Mitra, P. Bhimasankaram, Saroj B. MalikSingapore ;Hackensack, N.J. World Scientificc20101 online resource (464 p.)Series in algebra ;v. 10Description based upon print version of record.981-283-844-9 Includes bibliographical references and index.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. Applications16. Some Open Problems Appendix A Relations and Partial Orders; Bibliography; IndexThe 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...Series in algebra ;v. 10.MatricesLinear operatorsMatrices.Linear operators.515.7246Mitra Sujit Kumar12681Bhimasankaram P1573737Malik Saroj B1573738MiAaPQMiAaPQMiAaPQBOOK9910780881403321Matrix partial orders, shorted operators and applications3849615UNINA