Théorèmes de Perron-Frobenius et Stein-Rosenberg booléens

The eigenelements of a Boolean matrix are defined. A “normal form” is given, which allows one to characterize those Boolean matrices the (Boolean) spectral radius of which is 0 or 1. Then the following results are proved: a Boolean Perron-Frobenius theorem, a “Truncated” Boolean Stein-Rosenberg theorem, and a Boolean Stein-Rosenberg theorem, which are the exact Boolean analoques of the usual corresponding theorems concerning real nonnegative matrices. Applications of these results are given elsewhere.