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On three partial orderings of matrices. (English. English summary) Zbl 1065.15028
Summary: A new characterization and some properties for the sharp order of matrices are obtained using the core-nilpotent decomposition of matrices. The relation between the sharp partial ordering of nonnegative definite matrices and their squares is obtained. The relation between the star and the minus partial ordering of normal matrices is discussed. The related known results of Hermitian matrices are extended.

MSC:
15B48 Positive matrices and their generalizations; cones of matrices
15A45 Miscellaneous inequalities involving matrices
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