Matrix Partial Orders, Shorted Operators And Applications
Seiten
2010
World Scientific Publishing Co Pte Ltd (Verlag)
978-981-283-844-5 (ISBN)
World Scientific Publishing Co Pte Ltd (Verlag)
978-981-283-844-5 (ISBN)
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
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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Buch | Softcover (2022)
Springer Spektrum (Verlag)
CHF 55,95
