We obtain the formula [image omitted] for the inverse of polynomial maps of [image omitted] of the form [image omitted] where M(x) is a homogeneous of degree m nilpotent matrix, all of whose powers are exact; and we obtain recursion relations for the scalars cmk. Such maps have recently been considered by Connell and Zweibel, but our derivations is based on our earlier result that F-1(a) where x(tza) is the unique solution, with initial condition x(0za)=z, of the Wazewski differential equation dx/dt=Ft(x)-1a=a-M(x)a, with vector parameter a. Basic to our method is the multilinear matrix function B(xy,…z) uniquely determined by M(x). We give a new proof that all powers of M are exact provided only that both M and M2 are exact.
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