I have a 4x4 density matrix all of whose elements are nonzero. Its form is $$\begin{pmatrix} a & b & c & d \\ b^* & e & f & g \\ c^* & f^* & h & j \\ d^* & g^* & j^* & k \end{pmatrix}$$ where $a+e+h+k=1$, or in block form
$$\begin{pmatrix} A & B \\ B^\dagger & C \end{pmatrix}.$$
Is there simple way to find the eigenvalues and eigenvectors of this matrix?
I don't want to the largest or smallest eigenvalues. All the elements of the matrix are not a number. I calculated by help of the Mathematica and Maple (too much terms) but I want an analytical method.