On the bound of the eigenvalue in module for a positive tensor
The authors obtain a bound for a ratio of the largest eigenvalue and second largest eigenvalue in module for a higher-order tensor, following the definitions of eigenpairs introduced by \textit{L. Qi} [J. Symb. Comput. 40, No. 6, 1302--1324 (2005; Zbl 1125.15014)] and \textit{L. H. Lim} [``Singular values and eigenvalues of tensors: a variational approach'', in: Proceedings of the 1st IEEE international workshop on computational advances of multitensor adative processing. Piscataway, NJ: IEEE. 129--132 (2005; \url{doi:10.1109/CAMAP.2005.1574201})]. One can then deduce the bound of the second largest eigenvalue in module for a positive tensor, and the bound can reduce to the matrix cases. An inequality for \(H\)-eigenvalues is surmised.
scientific article; zbMATH DE number 6764697