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Harry Dym (2001)
International Journal of Applied Mathematics and Computer Science
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The purpose of this paper is to exhibit a connection between the Hermitian solutions of matrix Riccati equations and a class of finite dimensional reproducing kernel Krein spaces. This connection is then exploited to obtain minimal factorizations of rational matrix valued functions that are J-unitary on the imaginary axis in a natural way.
Lev Sakhnovich (2008)
Open Mathematics
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We consider the Knizhnik-Zamolodchikov system of linear differential equations. The coefficients of this system are rational functions generated by elements of the symmetric group n. We assume that parameter ρ = ±1. In previous paper [5] we proved that the fundamental solution of the corresponding KZ-equation is rational. Now we construct this solution in the explicit form.
Mehl, Christian, Mehrmann, Volker, Xu, Hongguo (2000)
ELA. The Electronic Journal of Linear Algebra [electronic only]
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Werner Gautschi (1954-1956)
Compositio Mathematica
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Kagan, Abram, Smith, Paul J. (1999)
Journal of Inequalities and Applications [electronic only]
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Lee, Anna (1985-1986)
Portugaliae mathematica
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Sternberg, Robert L. (1953)
Portugaliae mathematica
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Anderson, D.R., Moats, L.M. (2007)
Electronic Journal of Qualitative Theory of Differential Equations [electronic only]
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Tian, Yongge, Styan, George P.H. (2005)
Journal of Inequalities and Applications [electronic only]
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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....