Tournament matrix, Matrix square root, Doubly regular tournament
Fletcher asked whether there is a (0, 1)-matrix of order greater than 3 whose square is a regular tournament matrix. We give a negative answer for a special class of regular tournament matrices: There is no (0, 1)-matrix of order greater than 3 whose square is a doubly regular tournament matrix.
Hacioglu, Ilhan; Michael, T. S.; and Ozdemir, Serhat.
"Square roots of doubly regular tournament matrices",
Electronic Journal of Linear Algebra,