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Further properties of the star, left-star, right-star, and minus partial orderings. (English) Zbl 1048.15016
Authors’ abstract: Certain classes of matrices are indicated for which the star, left-star, right-star, and minus partial orderings, or some of them, are equivalent. Characterizations of the left-star and right-star orderings, similar to those devised by R. E. Hartwig and G. P. H. Styan [Linear Algebra Appl. 82, 145–161 (1986; Zbl 0603.15001)] for the star and minus orderings, are established along with other auxiliary results, which are of independent interest as well. Some inheritance-type properties of matrices are also given. The class of EP matrices appears to be essential in several points of our considerations.

15B48 Positive matrices and their generalizations; cones of matrices
15B57 Hermitian, skew-Hermitian, and related matrices
Full Text: DOI
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