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MATRIX PARTIAL ORDERS, SHORTED OPERATORS AND APPLICATIONS
by Sujit Kumar Mitra∗ (Indian Statistical Institute, India) , P Bhimasankaram (University of Hyderabad, India) , & Saroj B Malik (Hindu College, University of Delhi, India)
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
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