Extremal ranks of a quaternion matrix expression subject to consistent systems of quaternion matrix equations with applications
The authors consider the maximal and minimal ranks of the matrix function \(f(X_1,X_2)=A-A_3X_1B_3-A_4X_2B_4\) where the quaternion matrices \(X_1\), \(X_2\) are subject to the consistent systems of quaternion matrix equations \(A_1X_1=C_1\), \(X_1B_1=C_2~(*)\) and \(A_2X_2=C_3\), \(X_2B_2=C_4~(**)\). Interesting particular cases are the constrained matrix equations \(f=0\) or \(X_2=0\), \(f=0\) or \(B_1=A_1^*\), \(B_2=A_2^*\), \(f=0\), the constraints being defined by systems \((*)\) and \((**)\). As applications, they give necessary and sufficient conditions for the existence of solutions to some systems of quaternion matrix equations.
scientific article; zbMATH DE number 5115446
scientific article