  We examine connection matrices of Ising systems with long-rang interaction on
d-dimensional hypercube lattices of linear dimensions L. We express the
eigenvectors of these matrices as the Kronecker products of the eigenvectors
for the one-dimensional Ising system. The eigenvalues of the connection
matrices are polynomials of the d-th degree of the eigenvalues for the
one-dimensional system. We show that including of the long-range interaction
does not remove the degeneracy of the eigenvalues of the connection matrix. We
analyze the eigenvalue spectral density in the limit L go to \infty. In the
case of the continuous spectrum, for d < 3 we obtain analytical formulas that
describe the influence of the long-range interaction on the spectral density
and the crucial changes of the spectrum.
