The Polynomial Eigenvalue Problem (PEVP) is a generalization of the clasical eigenvalue problem in linear algebra. Its condition number measures the sensitivity of the output with respect to perturbations in the input and works as a pre-requisite for the existence of a good algorithm.

Here we prove that, for random (symmetric and non–symmetric) gaussian inputs, the condition number of the real PEVP is rather small.

The formulas for the expected condition number turn out to be closed and very simple!