The

A hard problem in Linear Algebra is to compute the inertia.
No method is known to get the inertia of a matrix exactly in general.
In this paper we show that
the inertia is hard for PL (* probabilistic logspace*)
and in some cases the inertia can be computed in PL.
We extend our result to some problems related to the inertia.
Namely, we show that matrix stability is complete
for PL and the inertia of symmetric matrices can be computed in PL.