On some properties of nonnegative weakly irreducible tensors

Abstract

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.

This paper has been withdrawn by the author

References in corpus (2)

• Finding the Spectral Radius of a Nonnegative Tensor
• A note on the geometric simplicity of the spectral radius of nonnegative irreducible tensors

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