# Expected value of the condition number of random matrices

I found in this article that $$\forall \Gamma$$ random matrix with i.i.d. gaussian $$(0,\sigma^2)$$ entrances $$\mathbb E [\kappa (\Gamma)]=+\infty$$ is that a property of the gaussian distribution or it can be generalized to more general random matrices? Because the proof works with gaussian distribution but I don't see I reason why that feature should be important in this case.