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

Abstract EN

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 equations A1X=C1,XB1=C2, and A3XA3*=C3.

Moreover, formulas of the maximal and minimal 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 applications, we give necessary and sufficient conditions for the quaternion matrix equations A1X=C1,XB1=C2,A3XA3*=C3, and A4XA4*=C4 to have real and complex Hermitian solutions.