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The common solution to six quaternion matrix equations with applications. (English) Zbl 1141.15016

The authors consider the system of six quaternion matrix equations \(A_1X=C_1\), \(XB_1=C_2\), \(A_2X=C_3\), \(XB_2=C_4\), \(A_3XB_3=C_5\), \(A_4XB_4=C_6\). They give necessary and sufficient conditions for the existence of a quaternion matrix solution and they give explicit formulas for that solution. As applications they present the symmetric, persymmetric and centrosymmetric solutions to certain systems of quaternion matrix equations. (An \(m\times n\) quaternion matrix \((a_{i,j})\) is symmetric, persymmetric or centrosymmetric if \(a_{i,j}\) equals respectively \(\bar{a}_{j,i}\), \(\bar{a}_{m-j+1,n-i+1}\) or \(a_{m-i+1,n-j+1}\).) The results are illustrated by examples.

MSC:

15A24 Matrix equations and identities
15B33 Matrices over special rings (quaternions, finite fields, etc.)
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