On weighted partial orderings on the set of rectangular complex matrices.

Li, Hanyu; Yang, Hu; Shao, Hua

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Matrix equalities and inequalities involving Khatri-Rao and Tracy-Singh sums.

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On the star partial ordering of normal matrices.

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Some remarks on operators preserving partial orders of matrices

Jan Hauke (2008)

Discussiones Mathematicae Probability and Statistics

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Stępniak [Linear Algebra Appl. 151 (1991)] considered the problem of equivalence of the Löwner partial order of nonnegative definite matrices and the Löwner partial order of squares of those matrices. The paper was an important starting point for investigations of the problem of how an order between two matrices A and B from different sets of matrices can be preserved for the squares of the corresponding matrices A² and B², in the sense of the Löwner partial ordering, the star partial...