On the matrix equation $XA+A{X}^T=0$, II: Type 0-I interactions

The matrix equation $XA+A{X}^T=0$ was recently introduced by De Ter'an and Dopico to study the dimension of congruence orbits. They reduced the study of this equation to a number of special cases, several of which have not been explicitly solved. In this note we obtain an explicit, closed-form solution in the difficult Type 0-I interaction case.