  In 2010, Cassidy and Vancliff extended the notion of a quadratic form on n
generators to the noncommutative setting. In this article, we suggest a notion
of rank for such noncommutative quadratic forms, where n = 2 or 3. Since
writing an arbitrary quadratic form as a sum of squares fails in this context,
our methods entail rewriting an arbitrary quadratic form as a sum of products.
In so doing, we find analogs for 2 x 2 minors and determinant of a 3 x 3 matrix
in this noncommutative setting.
