I have read that 10.000x10.000 is no problem for LAPACK or similar routines. I would like to know if N=20.000 or 40.000 is possible.
EDIT: I don't know if it is relevant, but the matrix is positive definite!
Also (less important) if you have done it, how long did it take? I hear diagonalization of a N=1000 random takes about 1s and the scaling is O(N^3).
Thank you