Extremal ranks of a quaternion matrix expression subject to consistent systems of quaternion matrix equations with applications
Copyright policy )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.
- Shanghai University China (People's Republic of)
- Shandong University of Finance and Economics China (People's Republic of)
- Shanghai University China (People's Republic of)
Vector spaces, linear dependence, rank, lineability, Matrices over special rings (quaternions, finite fields, etc.), Matrix equations and identities, minimal rank, Theory of matrix inversion and generalized inverses, linear matrix expression, system of quaternion matrix equations, maximal rank, generalized inverse
Vector spaces, linear dependence, rank, lineability, Matrices over special rings (quaternions, finite fields, etc.), Matrix equations and identities, minimal rank, Theory of matrix inversion and generalized inverses, linear matrix expression, system of quaternion matrix equations, maximal rank, generalized inverse
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