A matrix inequality
Russell C. Thompson (1976)
Commentationes Mathematicae Universitatis Carolinae
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Russell C. Thompson (1976)
Commentationes Mathematicae Universitatis Carolinae
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Journal of Inequalities and Applications [electronic only]
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Mathematical Problems in Engineering
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Miroslav Fiedler, Thomas L. Markham (1994)
Mathematica Slovaca
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Kagan, Abram, Smith, Paul J. (1999)
Journal of Inequalities and Applications [electronic only]
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Werner Gautschi (1954-1956)
Compositio Mathematica
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Xiang Zhang, Qing-Wen Wang, Xin Liu (2012)
Open Mathematics
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Let S be a given set consisting of some Hermitian matrices with the same size. We say that a matrix A ∈ S is maximal if A − W is positive semidefinite for every matrix W ∈ S. In this paper, we consider the maximal and minimal inertias and ranks of the Hermitian matrix function f(X,Y) = P − QXQ* − TYT*, where * means the conjugate and transpose of a matrix, P = P*, Q, T are known matrices and for X and Y Hermitian solutions to the consistent matrix equations AX =B and YC = D respectively....