This is the second in a series of three papers dealing with sums of squares
and hypoellipticity in the infinitely degenerate regime. We give sharp
conditions on the entries of a positive semidefinite NxN matrix function F on
n-dimensional Euclidean space, whose determinant vanishes only at the origin
and such that F is comparable to its diagonal matrix, in order that F is a
finite sum of squares of C^2,delta vector fields. We also consider slightly
more general decompositions in which a single quasiconformal term need not be a
sum of squares.