The 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 L�wner 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. This is followed by a study of the L�wner order and a limited treatment of majorization (there is an abundance of literature available on majorization). The authors also 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.

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This unique book can be recommended to anybody interested in matrix orders. It contains a lot of results hitherto dispersed in research papers or being unpublished work of the authors. Although written a bit from the perspective of Statistics, where many applications come from, it should be consulted by students and researchers, both working in matrix theory and practice. The book has few typographical errors. Its printing is excellent, making a very pleasant reading. Containing a number of exercises, it may also serve as a textbook for an advanced matrix course. --Image

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