  I consider a general block tridiagonal matrix and the corresponding transfer
matrix. By allowing for a complex Bloch parameter in the boundary conditions,
the two matrices are related by a spectral duality. As a consequence, I derive
some analytic properties of the exponents of the transfer matrix in terms of
the eigenvalues of the (non-Hermitian) block matrix. Some of them are the
single-matrix analogue of results holding for Lyapunov exponents of an ensemble
of block matrices, which occur in models of transport. The counting function of
exponents is related to winding numbers of eigenvalues. I discuss some
implications of duality on the distribution (real bands and complex arcs) and
the dynamics of eigenvalues.
