Bisymmetric and centrosymmetric solutions to systems of real quaternion matrix equations

Bisymmetric and Centrosymmetric Solutions to Systems of Real Quaternion Matrix Equations

A1X = C1, A1X = C1, XB3 = C3, A2X = 62, to have bisymmetric solutions, and the system A1X = Ca, A3X B3 = C3, to have centrosymmetric solutions. The expressions of such solutions of the matrix and the systems mentioned above are also given. Moreover a criterion for a quaternion matrix to be bisymmetric is established and some auxiliary results on other sets over H are also mentioned. ~) 2005 Els...

The least-square bisymmetric solution to a quaternion matrix equation with applications

In this paper, we derive the necessary and sufficient conditions for the quaternion matrix equation XA=B to have the least-square bisymmetric solution and give the expression of such solution when the solvability conditions are met. Futhermore, we consider the maximal and minimal inertias of the least-square bisymmetric solution to this equation. As applications, we derive sufficient and necess...

Erratum to "The Real and Complex Hermitian Solutions to a System of Quaternion Matrix Equations with Applications"

We establish necessary and sufficient conditions for the existence of and the expressions for the general real and complex Hermitian solutions to the classical system of quaternion matrix equationsA1X C1, XB1 C2, and A3XA3 C3. Moreover, formulas of the maximal andminimal ranks of four real matrices X1, X2, X3, and X4 in solution X X1 X2i X3j X4k to the system mentioned above are derived. As app...

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

Ranks of the common solution to some quaternion matrix equations with applications

We derive the formulas of the maximal andminimal ranks of four real matrices $X_{1},X_{2},X_{3}$ and $X_{4}$in common solution $X=X_{1}+X_{2}i+X_{3}j+X_{4}k$ to quaternionmatrix equations $A_{1}X=C_{1},XB_{2}=C_{2},A_{3}XB_{3}=C_{3}$. Asapplications, we establish necessary and sufficient conditions forthe existence of the common real and complex solutions to the matrixequations. We give the exp...