LEADER 03167nam 2200637 a 450 001 9910808928603321 005 20230725041540.0 010 $a1-282-75761-X 010 $a9786612757617 010 $a981-283-845-7 035 $a(CKB)2490000000001864 035 $a(EBL)731077 035 $a(OCoLC)671654997 035 $a(SSID)ssj0000422831 035 $a(PQKBManifestationID)12209492 035 $a(PQKBTitleCode)TC0000422831 035 $a(PQKBWorkID)10432624 035 $a(PQKB)10551664 035 $a(MiAaPQ)EBC731077 035 $a(WSP)00007170 035 $a(Au-PeEL)EBL731077 035 $a(CaPaEBR)ebr10422474 035 $a(CaONFJC)MIL275761 035 $a(EXLCZ)992490000000001864 100 $a20100823d2010 uy 0 101 0 $aeng 135 $aurcn||||||||| 181 $ctxt 182 $cc 183 $acr 200 10$aMatrix partial orders, shorted operators and applications$b[electronic resource] /$fSujit Kumar Mitra, P. Bhimasankaram, Saroj B. Malik 210 $aSingapore ;$aHackensack, N.J. $cWorld Scientific$dc2010 215 $a1 online resource (464 p.) 225 1 $aSeries in algebra ;$vv. 10 300 $aDescription based upon print version of record. 311 $a981-283-844-9 320 $aIncludes bibliographical references and index. 327 $aPreface; 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 327 $a16. Some Open Problems Appendix A Relations and Partial Orders; Bibliography; Index 330 $aThe present monograph on matrix partial orders, appearing for the first time, is a unique presentation of many partial orders on matrices that have fascinated mathematicians for their beauty and applied scientists for their wide-ranging application potential. Except for the Lowner order, the partial orders considered are relatively new and came into being in the late 1970's. After a detailed introduction to generalized inverses and decompositions, the three basic partial orders - namely, the minus, the sharp and the star - and the corresponding one-sided orders are presented using various... 410 0$aSeries in algebra ;$vv. 10. 606 $aMatrices 606 $aLinear operators 615 0$aMatrices. 615 0$aLinear operators. 676 $a515.7246 700 $aMitra$b Sujit Kumar$012681 701 $aBhimasankaram$b P$01710748 701 $aMalik$b Saroj B$01710749 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910808928603321 996 $aMatrix partial orders, shorted operators and applications$94101603 997 $aUNINA