  A hitherto difficult and unsolved issue in plasma physics is how to give a
general numerical solver for complicated plasma dispersion relation, although
we have long known the general analytical forms. We transform the task to a
full-matrix eigenvalue problem, which allows to numerically calculate all the
dispersion relation solutions exactly free from convergence problem and give
polarizations naturally for arbitrarily complicated multi-scale fluid plasma
with arbitrary number of components. Attempt to kinetic plasma via $N$-point
Pad\'e approximation of plasma dispersion function also shows good results.
