We give a Brualdi-type Z-eigenvalue inclusion set of tensors,and prove that it is tighter than the inclusion set given by G.Wang,G.L.Zhou,and L.Caccetta[Discrete Contin.Dyn.Syst.Ser.B,2017,22:187–198]in a special cas...We give a Brualdi-type Z-eigenvalue inclusion set of tensors,and prove that it is tighter than the inclusion set given by G.Wang,G.L.Zhou,and L.Caccetta[Discrete Contin.Dyn.Syst.Ser.B,2017,22:187–198]in a special case.We also give an inclusion set for l^k,s-singular values of rectangular tensors.展开更多
We show that a connected uniform hypergraph G is odd-bipartite if and only if G has the same Laplacian and signless Laplacian Z-eigenvalues. We obtain some bounds for the largest （signless） Laplacian Z-eigenvalue of...We show that a connected uniform hypergraph G is odd-bipartite if and only if G has the same Laplacian and signless Laplacian Z-eigenvalues. We obtain some bounds for the largest （signless） Laplacian Z-eigenvalue of a hypergraph. For a k-uniform hyperstar with d edges （2d ≥ k ≥ 3）, we show that its largest （signless） Laplacian Z-eigenvalue is d.展开更多
In this paper,we present several sharper upper bounds for the M-spectral radius and Z-spectral radius based on the eigenvalues of some unfolding matrices of nonnegative tensors.Meanwhile,we show that these bounds coul...In this paper,we present several sharper upper bounds for the M-spectral radius and Z-spectral radius based on the eigenvalues of some unfolding matrices of nonnegative tensors.Meanwhile,we show that these bounds could be tight for some special tensors.For a general nonnegative tensor which can be transformed into a matrix,we prove the maximal singular value of this matrix is an upper bound of its Z-eigenvalues.Some examples are provided to show these proposed bounds greatly improve some existing ones.展开更多
基金This work was supported in part by the National Natural Science Foundation of China(Grant No.11801115)the Youth Science Foundation of Heilongjiang Province of China(No.QC2018002)the Fundamental Research Funds for Central Universities.
文摘We give a Brualdi-type Z-eigenvalue inclusion set of tensors,and prove that it is tighter than the inclusion set given by G.Wang,G.L.Zhou,and L.Caccetta[Discrete Contin.Dyn.Syst.Ser.B,2017,22:187–198]in a special case.We also give an inclusion set for l^k,s-singular values of rectangular tensors.
基金Acknowledgements Foundation of China This work was supported by the National Natural Science （Grant Nos. 11371109, 11426075）, the Natural Science Foundation of tteilongjiang Province （No. QC2014C001）, ：and the Fundamental Research Funds for the Central Universities
文摘We show that a connected uniform hypergraph G is odd-bipartite if and only if G has the same Laplacian and signless Laplacian Z-eigenvalues. We obtain some bounds for the largest （signless） Laplacian Z-eigenvalue of a hypergraph. For a k-uniform hyperstar with d edges （2d ≥ k ≥ 3）, we show that its largest （signless） Laplacian Z-eigenvalue is d.
基金the National Natural Science Foundation of China(No.11271206)the Natural Science Foundation of Tianjin(No.12JCYBJC31200).
文摘In this paper,we present several sharper upper bounds for the M-spectral radius and Z-spectral radius based on the eigenvalues of some unfolding matrices of nonnegative tensors.Meanwhile,we show that these bounds could be tight for some special tensors.For a general nonnegative tensor which can be transformed into a matrix,we prove the maximal singular value of this matrix is an upper bound of its Z-eigenvalues.Some examples are provided to show these proposed bounds greatly improve some existing ones.
