非负弱不可约张量的若干性质
On some properties of nonnegative weakly irreducible tensors
AI总结：
本文通过证明一个基本引理，将非负不可约张量的若干结论推广到非负弱不可约张量，并给出反例说明部分结论不成立。
摘要：
本文主要关注如何将非负不可约张量的一些结论推广到非负弱不可约张量。为此，使用新工具证明了一个基本且重要的引理。首先，我们给出了随机张量的定义。然后，我们证明了每个谱半径为1的非负弱不可约张量都对角相似于唯一的弱不可约随机张量。在此基础上，我们证明了一些重要的引理，这些引理有助于推广相关结果。提供了一些反例，说明非负不可约张量的某些结论对于非负弱不可约张量不成立。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
