Matrix Partial Orders, Shorted Operators And Applications - P Bhimasankaram, Saroj B Malik, Sujit Kumar Mitra

Matrix Partial Orders, Shorted Operators And Applications

Buch | Hardcover
464 Seiten
2010
World Scientific Publishing Co Pte Ltd (Verlag)
978-981-283-844-5 (ISBN)
123,45 inkl. MwSt
An introduction to generalized inverses and decompositions. It presents the three basic partial orders - namely, the minus, the sharp and the star - and the corresponding one-sided orders using various generalized inverses. It gives a unified theory of these partial orders.
The present monograph on matrix partial orders, the first on this topic, makes 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 Löwner order, the partial orders considered are relatively new and came into being in the late 1970s. 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 generalized inverses. The authors then give a unified theory of all these partial orders as well as study the parallel sums and shorted matrices, the latter being studied at great length. Partial orders of modified matrices are a new addition. Finally, applications are given in statistics and electrical network theory.∗Deceased

Introduction; Decompositions and Generalized Inverses; Minus Order; Sharp Order; Star Order; One-Sided Orders; Lowner Order and Majorization; Unified Theory of Matrix Partial Orders through Generalized Inverses; Parallel Sums; Schur Complements and Shorted Operators; Shorted Operators II; Supremum and Infimum for a Pair of Matrices; Partial Orders for Modified Matrices; Statistics; Electrical Network Theory.

Erscheint lt. Verlag 1.4.2010
Reihe/Serie Series In Algebra ; 10
Verlagsort Singapore
Sprache englisch
Themenwelt Mathematik / Informatik Mathematik Algebra
Mathematik / Informatik Mathematik Logik / Mengenlehre
ISBN-10 981-283-844-9 / 9812838449
ISBN-13 978-981-283-844-5 / 9789812838445
Zustand Neuware
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