In this paper we show how some difficult linear algebra problems can be “approximately” solved using statistical learning methods. We illustrate our results by considering the state and output feedback, finite-time robust stabilization problems for linear systems subject to time-varying norm-bounded uncertainties and to unknown disturbances. In the state feedback case, the paper provides a sufficient condition for finite-time stabilization in the presence of time-varying disturbances; such condition requires the solution of a linear matrix inequality (LMI) feasibility problem, which is by now a standard application of linear algebraic methods. In the output feedback case, however, we end up with a bilinear matrix inequality (BMI) problem which we tackle by resorting to a statistical approach.