Sharp bounds for spectral radius of nonnegative weakly irreducible tensors

doi:10.1007/s11464-019-0797-1

Front. Math. China

2019, Vol. 14

Issue (5) : 989-1015 https://doi.org/10.1007/s11464-019-0797-1

RESEARCH ARTICLE

Sharp bounds for spectral radius of nonnegative weakly irreducible tensors

Lihua YOU¹, Xiaohua HUANG¹, Xiying YUAN²(

)

¹. School of Mathematical Sciences, South China Normal University, Guangzhou 510631, China
². Department of Mathematics, Shanghai University, Shanghai 200444, China

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Abstract

We obtain the sharp upper and lower bounds for the spectral radius of a nonnegative weakly irreducible tensor. By using the technique of the representation associate matrix of a tensor and the associate directed graph of the matrix, the equality cases of the bounds are completely characterized by graph theory methods. Applying these bounds to a nonnegative irreducible matrix or a connected graph (digraph), we can improve the results of L. H. You, Y. J. Shu, and P. Z. Yuan [Linear Multilinear Algebra, 2017, 65(1): 113–128], and obtain some new or known results. Applying these bounds to a uniform hypergraph, we obtain some new results and improve some known results of X. Y. Yuan, M. Zhang, and M. Lu [Linear Algebra Appl., 2015, 484: 540–549]. Finally, we give a characterization of a strongly connected k-uniform directed hypergraph, and obtain some new results by applying these bounds to a uniform directed hypergraph.

Keywords Nonnegative weakly irreducible tensors uniform (directed) hyper- graph spectral radius bound

Corresponding Author(s): Xiying YUAN

Issue Date: 22 November 2019

Cite this article:

Lihua YOU,Xiaohua HUANG,Xiying YUAN. Sharp bounds for spectral radius of nonnegative weakly irreducible tensors[J]. Front. Math. China, 2019, 14(5): 989-1015.

URL:

https://academic.hep.com.cn/fmc/EN/10.1007/s11464-019-0797-1
https://academic.hep.com.cn/fmc/EN/Y2019/V14/I5/989

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