Convergence of inhomogenous products of matrices and coefficients of ergodicity Original Research Article

Given a square matrix A and a norm double vertical bar double vertical bar, the coefficient of ergodicity of A with respect to double vertical bar double vertical bar is defined as max image, double vertical barxdouble vertical bar = 1, xTF = 0} with F as a matrix satisfying AF = 0. We demonstrate that for a bounded set of such matrices with all coefficients of ergodicity of the matrices in the set below 1, all sequences constructed through inhomogenous products of matrices from the set converge geometrically.