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In this paper, some necessary and sufficient conditions are established for the constraint generalized Sylvester matrix equations to have a common solution. The expression of the general common solution is also given under the solvable conditions. In addition, a numerical example is presented to illustrate the presented theory.
Let Hm×n be the set of all m × n matrices over the real quaternion algebra H={c0+c1i+c2j+c3k∣i2=j2=k2=ijk=−1,c0,c1,c2,c3∈R}. A∈Hn×n is known to be η-Hermitian if A=Aη*=−ηA*η,η∈{i,j,k} and A * means the conjugate transpose of A. We mention some necessary and sufficient conditions for the existence of the solution to the system of real quaternion matrix equations including η-Hermicity A1X=C1,A2Y=C2,YB2=D2,Y=Yη*,A3Z=C3,ZB3=D3,Z=Zη*,A4X+(A4X)η*+B4YB4η*+C4ZC4η*=D4,...
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