Solution to a system of real quaternion matrix equations encompassing η-Hermicity

Abstract

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-HermicityA1X=C1,A2Y=C2,YB2=D2,Y=Yη*,A3Z=C3,ZB3=D3,Z=Zη*,A4X+(A4X)η*+B4YB4η*+C4ZC4η*=D4,and also construct the general solution to the system when it is consistent. The outcome of this paper diversifies some particular results in the literature. Furthermore, we constitute an algorithm and a numerical example to comprehend the approach established in this treatise.