Products of 2.2 Random Matrices

The notion of the shape of a triangle can be used to define the shape of a 2.2 real matrix; we find that the shape of a matrix retains just the right amount of information required for determining the main features of the asymptotic behaviour, as n.., of GnGn.1.G1, where the Gi are i.i.d. copies of a 2.2 random matrix G. An alternative formula to the Furstenberg formula is proposed for the upper Lyapounov exponent of the probability distribution of G. We find that in some cases, using our formula, the Lyapounov exponent is more susceptible to explicit calculation.