The Strength of Non-Perturbative Effects in Matrix Models and String Effective Lagrangians

We present a summary of the results of an explicit calculation of the strength of non-perturbative interactions in matrix models and string effective Lagrangians. These interactions are induced by single eigenvalue instantons in the $d=1$ bosonic matrix model. A well defined approximation scheme is used to obtain induced operators whose exact form we exhibit. We briefly discuss the possibility that similar instantons in a supersymmetric version of the theory may break supersymmetry dynamically.