Extremal ranks of a quaternion matrix expression subject to consistent matrix equations with applications

摘要

Assume that the linear quaternion matrix expression f(X,Y)=A-B1XC1 -B2YC2 where X,Y are variant quaternion matrices and the given matrices satisfy R(B1) (C)R(B2),R(CT2)(C)R(CT1).. In this paper, we derive the maximal and minimal ranks of f(X, Y) subject to the consistent quaternion matrix equations B3XC3=A3,B4YC4=A4 respectively. As an application, we get the necessary and sufficient conditions for the consistence of the system of quaternion matrix equitation: B3XC}=A} B4YC4=A4 and. B1XC1+B2YC2=A.