  In this paper the partition function of N=4 D=0 super Yang-Mills matrix
theory with arbitrary simple gauge group is discussed. We explicitly computed
its value for all classical groups of rank up to 11 and for the exceptional
groups G_2, F_4 and E_6. In the case of classical groups of arbitrary rank we
conjecture general formulas for the B_r, C_r and D_r series in addition to the
known result for the A_r series. Also, the relevant boundary term contributing
to the Witten index of the corresponding supersymmetric quantum mechanics has
been explicitly computed as a simple function of rank for the orthogonal and
symplectic groups SO(2N+1), Sp(2N), SO(2N).
