The Perron-Frobenius Theorem and the Ranking of Football Teams

PERRON-FROBENIUS THEORY ON THE NUMERICAL RANGE FOR SOME CLASSES OF REAL MATRICES

We give further results for Perron-Frobenius theory on the numericalrange of real matrices and some other results generalized from nonnegative matricesto real matrices. We indicate two techniques for establishing the main theorem ofPerron and Frobenius on the numerical range. In the rst method, we use acorresponding version of Wielandt's lemma. The second technique involves graphtheory.

The Sign-Real Spectral Radius for Real Tensors

In this paper a new quantity for real tensors, the sign-real spectral radius, is defined and investigated. Various characterizations, bounds and some properties are derived. In certain aspects our quantity shows similar behavior to the spectral radius of a nonnegative tensor. In fact, we generalize the Perron Frobenius theorem for nonnegative tensors to the class of real tensors.

Some results on the block numerical range

The main results of this paper are generalizations of classical results from the numerical range to the block numerical range. A different and simpler proof for the Perron-Frobenius theory on the block numerical range of an irreducible nonnegative matrix is given. In addition, the Wielandt's lemma and the Ky Fan's theorem on the block numerical range are extended.

Description and Analysis of Performance, Potential and Efficiency of Iranian football pro- league by Data Envelopment Analysis

In the case of football it could be argued that the purpose of teams is to win the competitions in which they participated. However, the assessment of  football teams from the efficiency aspect would be relevant in judging whether the results have been obtained without waste. The purpose of this research is to compare  and  analysis of league ranking with  Potential and efficiency ranking. The ...

Spectrum Properties of the Koopman and Frobenius-Perron Operators