Frontiers of Mathematics in China >
Sharp bounds for spectral radius of nonnegative weakly irreducible tensors
Received date: 18 Jun 2019
Accepted date: 08 Oct 2019
Published date: 15 Oct 2019
Copyright
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.
Lihua YOU , Xiaohua HUANG , Xiying YUAN . Sharp bounds for spectral radius of nonnegative weakly irreducible tensors[J]. Frontiers of Mathematics in China, 2019 , 14(5) : 989 -1015 . DOI: 10.1007/s11464-019-0797-1
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