  Motivated by the theory of inhomogeneous Markov chains, we determine a
sufficient condition for the convergence to 0 of a general product formed from
a sequence of real or complex matrices. When the matrices have a common
invariant subspace $H$, we give a sufficient condition for the convergence to 0
on $H$ of a general product. Our result is applied to obtain a condition for
the weak ergodicity of an inhomogeneous Markov chain. We compare various types
of contractions which may be defined for a single matrix, such as
paracontraction, $l$--contraction, and $H$--contraction, where $H$ is an
invariant subspace of the matrix.
