An analysis of the matrix equation AX + X̄B = C

Resumo

The matrix equation AX + X̄B = C, where X̄B is obtained by the entry-wise conjugation of X, is examined. On the basis of analogy with the Sylvester matrix equation, special cases are distinguished where the former equation corresponds to normal and self-adjoint Sylvester equations. Efficient numerical algorithms are proposed for these special cases.