On the Construction of Zero Energy States in Supersymmetric Matrix Models

For the SU(N) invariant supersymmetric matrix model related to membranes in 4 space-time dimensions, the general solution to the equation(s) $Q^{\dagger}\Psi=0$ $(Q\chi =0)$ is determined for N odd. For any such (bosonic) solution of $Q^{\dagger}\Psi=0$, a (fermionic) $\Phi$ is found that (formally) satisfies $Q^{\dagger}\Phi=\Psi$. For the analogous model in 11 dimensions the solution of $Q^{\dagger}\Psi=0 (Q\Psi=0)$ is outlined.