On the Matrix Equation XA + AX_T = 0, II

Abstract

The matrix equation $XA + AX^T = 0$ was recently introduced by De Ter\\u27an 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