Sharp bounds for spectral radius of nonnegative weakly irreducible tensors  

作　　者：Lihua YOU Xiaohua HUANG Xiying YUAN 

机构地区：[1]School of Mathematical Sciences,South China Normal University,Guangzhou 510631,China [2]Department of Mathematics,Shanghai University,Shanghai 200444,China

出　　处：《Frontiers of Mathematics in China》2019年第5期989-1015,共27页中国高等学校学术文摘·数学（英文）

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.

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.

关 键 词：NONNEGATIVE WEAKLY IRREDUCIBLE TENSORS uniform(directed)hypergraph spectral radius BOUND 

分 类 号：O15[理学—数学]