The Finite-step Realization of the Joint Spectral Radius of a Pair of n x n Special Matrices.

A set of matrices is said to have the finiteness property if the maximal rate of growth of long products of matrices taken from the set can be obtained by a periodic product. It studies the finite - step realization of the joint generalized spectral radius of a pair of real square matrices. If S = | S₁, S₂ % where S₁, S₂ are n xn matrices and S₁ = ( a_ij ) with a_ij 0 and S₂ is similar to a diagonal matrix whose nonzero elements have the same sign, S has the finitenes property. [ABSTRACT FROM AUTHOR]