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Characterizations of minus and star orders between the squares of Hermitian matrices. (English) Zbl 1061.15018

The paper deals with the minus and star partial orders between the squares of Hermitian matrices.
J. Groß [ibid. 326, 215–223 (2001; Zbl 0979.15019)], developed characterizations of the minus and star partial orders between the squares of Hermitian nonnegative definite matrices referring to the concept of the space preordering.
In this paper, the authors generalize the results of L. Groß by deleting the nonnegative definiteness assumption. The characterization of \(A^2 \bar{\leq} B^2\), is similar to the obtained by L. Groß. However, the characterization of the star partial order between \(A^2\) and \(B^2\), shown in this paper, changes substantially with respect to the one proved by L. Groß.

MSC:

15B48 Positive matrices and their generalizations; cones of matrices
15A45 Miscellaneous inequalities involving matrices
15B57 Hermitian, skew-Hermitian, and related matrices

Citations:

Zbl 0979.15019
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References:

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