A MAX VERSION OF PERRON-FROBENIUS THEOREM FOR NONNEGATIVE TENSOR

In this paper we generalize the max algebra system of nonnegative matrices to the class of nonnegative tensors and derive its fundamental properties. If A is an element of R-+([m,n]) is a nonnegative essentially positive tensor such that satisfies the condition class NC, we prove that there exist mu(A) and a corresponding positive vector x such that max (1<i2...im<n){a(ii2)...i(m)x(i2)...x(im)} = mu(A)x(i)(m-1), i = 1,2,...,n. This theorem, is well known as the max algebra version of Perron-Frobenius theorem for this new system.