  The eigenvalue equation of a band or a block tridiagonal matrix, the tight
binding model for a crystal, a molecule, or a particle in a lattice with random
potential or hopping amplitudes: these and other problems lead to three-term
recursive relations for (multicomponent) amplitudes. Amplitudes n steps apart
are linearly related by a transfer matrix, which is the product of n matrices.
Its exponents describe the decay lengths of the amplitudes. A formula is
obtained for the counting function of the exponents, based on a duality
relation and the Argument Principle for the zeros of analytic functions. It
involves the corner blocks of the inverse of the associated Hamiltonian matrix.
As an illustration, numerical evaluations of the counting function of quasi 1D
Anderson model are shown.
