On some properties of nonnegative weakly irreducible tensors
Spectral Theory
2012-03-14 v3 Numerical Analysis
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.
Keywords
Cite
@article{arxiv.1111.0713,
title = {On some properties of nonnegative weakly irreducible tensors},
author = {Yuning Yang and Qingzhi Yang},
journal= {arXiv preprint arXiv:1111.0713},
year = {2012}
}
Comments
This paper has been withdrawn by the author