I have a 4x4 density matrix (Trace 1) whose elements are nonzero. Its form is

a  b  c  d

b* e  f  g

c* f* h  j

d* g* j* k

where a+e+h+k=1.

Is there a simple way to find eigenvalues and eigenvectors of this matrix?  I calculated in Mathematicai Maple, MATLAB (There are too much terms). More simple way?