An eigenvalue localization set for tensors and its applications.
A new eigenvalue localization set for tensors is given and proved to be tighter than those presented by Liet al. (Linear Algebra Appl. 481:36-53, 2015) and Huanget al. (J. Inequal. Appl. 2016:254, 2016). As an application of this set, new bounds for the minimum eigenvalue of [Formula: see text]-tensors are established and proved to be sharper than some known results. Compared with the results obtained by Huanget al., the advantage of our results is that, without considering the selection of nonempty proper subsetsSof [Formula: see text], we can obtain a tighter eigenvalue localization set for tensors and sharper bounds for the minimum eigenvalue of [Formula: see text]-tensors. Finally, numerical examples are given to verify the theoretical results.
College of Data Science and Information Engineering, Guizhou Minzu University, Guiyang, Guizhou 550025 P.R. China.
Jianxing
0000-0001-5938-3518
J
Zhao
College of Data Science and Information Engineering, Guizhou Minzu University, Guiyang, Guizhou 550025 P.R. China.
Caili
C
Sang
[Formula: see text]-tensors; localization set; minimum eigenvalue; nonnegative tensors