Sharp bounds for spectral radius of nonnegative weakly irreducible tensors
作者机构：School of Mathematical SciencesSouth China Normal UniversityGuangzhou 510631China Department of MathematicsShanghai UniversityShanghai 200444China
出 版 物：《Frontiers of Mathematics in China》 (中国高等学校学术文摘·数学（英文）)
年 卷 期：2019年第14卷第5期
页 面：989-1015页
核心收录：
基 金：This work was supported by the National Natural Science Foundation of China(Grant Nos.11571123,11871040,11971180) the Guangdong Provincial Natural Science Foundation(No.2015A030313377) Guangdong Engineering Research Center for Data Science.
主 题：Nonnegative weakly irreducible tensors uniform(directed)hypergraph spectral radius bound
摘 要：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/c-uniform directed hypergraph,and obtain some new results by applying these bounds to a uniform directed hypergraph.
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