On the matrix equation $$ X\bar X = \bar XX $$
Х. Д. Икрамов · Moscow University Computational Mathematics and Cybernetics · 2010
It is shown that every solution to the equation $$ X\bar X = \bar XX $$ can be reduced by a real orthogonal similarity transformation to a block triangular form with diagonal blocks of orders one and two. If the solution X is a normal matrix, then its block triangular form is actually a block diagonal. In this case, the form of the diagonal blocks is found, yielding new proof of the recent results of Goodson and Horn.