Expressions for Permanent of a Matrix Given that the permanent of a matrix can be written in a similar form as the determinant, as a sum of permutations of the elements of the matrix, is there also a relationship between the permanent and the eigenvalues of the matrix? Analogous to the determinant given by the product of eigenvalues?
Also, does anyone know of a comprehensive reference on matrix permanents? It's hard to find a good one (maybe it's just because there isn't a lot written on them.)

There can't really be a simple relationship, because the permanent is basis-dependent whilst the eigenvalues are not.
For example, $$\pmatrix{1 & 1 \\ -1 & 1}^{-1} \pmatrix{1 & 2 \\ 2 & 1} \pmatrix{1 & 1 \\ -1 & 1} = \pmatrix{-1 & 0 \\ 0 & 3}$$
transforms from permanent $1+4=5$ to $-3$.
