Geodesic
Some results on matrix partial orderings and reverse order law
The electronic journal of linear algebra, Tome 20 (2010), pp. 254-273.

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Summary: Some results relating different matrix partial orderings and the reverse order law for the Moore-Penrose inverse and the group inverse are given. Special attention is paid when at least one of the two involved matrices is EP.
Classification : 15A09, 15A57
Keywords: partial ordering, Moore-Penrose inverse, group inverse, reverse order law 
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     title = {Some results on matrix partial orderings and reverse order law},
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Benitez, Julio; Liu, Xiaoji; Zhong, Jin. Some results on matrix partial orderings and reverse order law. The electronic journal of linear algebra, Tome 20 (2010), pp. 254-273. http://geodesic.mathdoc.fr/item/ELA_2010__20__a35/