  A square, upper-triangular matrix U is a Cholesky root of a matrix M provided
U*U=M, where * represents the conjugate transpose. Over finite fields, as well
as over the reals, it suffices for U^TU=M. In this paper, we investigate the
number of such factorizations over the finite field with two elements, F2, and
prove the existence of a rank-preserving bijection between the number of
Cholesky roots of the zero matrix and the upper-triangular square roots the
zero matrix.
