Matrix partial orders, shorted operators and applications
著者
書誌事項
Matrix partial orders, shorted operators and applications
（Series in algebra, v. 10）
World Scientific, c2010
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注記
Includes bibliographical references (p. 439-443) and index
内容説明・目次
内容説明
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 Loewner 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
目次
- 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.
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