  Given an i.i.d. sequence $\{A_n(\omega)\}_{n\ge 1}$ of invertible matrices
and a random matrix $B(\omega)$, we consider the random matrix sequences
inductively defined by $S_n(\omega) = A_n(\omega)S_{n-1}(\omega)$ and
$T_n(\omega) =
B(\sigma^{n-1}\omega)S_{n-1}(\omega)+A_n(\omega)T_{n-1}(\omega)$, and study
several limit theorems involving $T_n(\omega)$ as well as the asymptotic
behaviour of the action of $T_n(\omega)$ on the projective space and on the
unit circle.
