Théorèmes de Perron-Frobenius et Stein-Rosenberg booléens |
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Authors: | François Robert |
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Affiliation: | Institut National Polytechnique Laboratoire de Mathématiques Appliquées Tour des Mathématiques B.P. 53—38041 Grenoble, France |
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Abstract: | 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. |
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