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\( \eta \)-Hermitian solution to a system of quaternion matrix equations. (English) Zbl 1452.15007

Summary: For \(\eta \in \{\mathbf{i},\mathbf{j},\mathbf{k}\} \), a real quaternion matrix \(A\) is said to be \(\eta \)-Hermitian if \(A=A^{\eta *}\), where \(A^{\eta *}=-\eta A^*\eta \), and \(A^*\) stands for the conjugate transpose of \(A\). In this paper, we present some practical necessary and sufficient conditions for the existence of an \(\eta \)-Hermitian solution to a system of constrained two-sided coupled real quaternion matrix equations and provide the general \(\eta \)-Hermitian solution to the system when it is solvable. Moreover, we present an algorithm and a numerical example to illustrate our results.

MSC:

15A24 Matrix equations and identities
15A09 Theory of matrix inversion and generalized inverses
15B33 Matrices over special rings (quaternions, finite fields, etc.)
15B57 Hermitian, skew-Hermitian, and related matrices
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