The theory of the eigenvalue spectrum of a system consisting of a Hamiltonian with a random part H and a non‐random term H0is considered. The random part consists of matrix elements which are distributed independently of one another with a Gaussian distribution, but the non‐random part is quite general. An information theoretic argument is used to derive the joint distribution of eigenvalues and a sufficient conduction for a localization is obtained. Essentially this is that the spacing of nearest neighbor eigenvalues in the two matrices should be equal. Attention is drawn to similar phenomena in nuclear physics and it is suggested that such an Anderson‐Mott transition may in fact occur in these systems.