  The results of [I. Ojeda, Amer. Math. Monthly, 122, pp 60--64] provides a
characterization of Kronecker square roots of matrices in terms of the symmetry
and rank of the block vec matrix (rearrangement matrix). In this short note we
reformulate the characterization in terms of rank only by considering an
alternative to the block vec matrix, provided that the characteristic of the
underlying field is not equal to 2.
