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The eigenvalue equation of a band or a block tridiagonal matrix, the tightbinding model for a crystal, a molecule, or a particle in a lattice with randompotential or hopping amplitudes: these and other problems lead to three-termrecursive relations for (multicomponent) amplitudes. Amplitudes n steps apartare linearly related by a transfer matrix, which is the product of n matrices.Its exponents describe the decay lengths of the amplitudes. A formula isobtained for the counting function of the exponents, based on a dualityrelation and the Argument Principle for the zeros of analytic functions. Itinvolves the corner blocks of the inverse of the associated Hamiltonian matrix.As an illustration, numerical evaluations of the counting function of quasi 1DAnderson model are shown.

Counting the exponents of single transfer matrices