Reproducing kernels and Riccati equations

Harry Dym

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Dual Szegő pairs of sequences of rational matrix-valued functions.

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Necessary and sufficient conditions for the existence of a Hermitian positive definite solution of a type of nonlinear matrix equations.

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A theorem on Hermitian solutions for related matrix differential and integral equations

Sternberg, Robert L. (1953)

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Inertias and ranks of some Hermitian matrix functions with applications

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....