On some properties of nonnegative weakly irreducible tensors

Details On some properties of nonnegative weakly irreducible tensors On some properties of nonnegative weakly irreducible tensors

2011-11-03

arxiv.org/abs/1111.0713v3

Mathematics

Spectral Theory

This paper has been withdrawn by the author

Scientific paper

In this paper, we mainly focus on how to generalize some conclusions from nonnegative irreducible tensors to nonnegative weakly irreducible tensors. To do so, a basic and important lemma is proven using new tools. First, we give the definition of stochastic tensors. Then we show that every nonnegative weakly irreducible tensor with spectral radius being one is diagonally similar to a unique weakly irreducible stochastic tensor. Based on it, we prove some important lemmas, which help us to generalize the results related. Some counterexamples are provided to show that some conclusions for nonnegative irreducible tensors do not hold for nonnegative weakly irreducible tensors.

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