# Closed form for singular values of 2D Laplacian?

Does anyone know where to find an analytic form for the singular values of the finite-difference approximation to the 2D Laplacian, expressed in matrix form for a square grid? This would be for the standard 5-point FD approximation.

I've found the eigenvalues (they are $\sin^2$ functions), but have not seen expressions for the singular values.

Thanks, Tom