LAUSR

The -congruence Sylvester equation is the matrix equation , where , and are given, whereas is to be determined. Here, or , and (transposed) or (conjugate transposed). Very recently, Satake et al. showed that under some conditions, the matrix equation for the case is equivalent to the generalized Sylvester equation. In this paper, we demonstrate that the result can be extended to the case . Through this extension, the least squares solution of the -congruence Sylvester equation may be obtained using well-researched results on the least squares solution of the generalized Sylvester equation.