A new eigenvalue inclusion set for tensors and its applications

作者：Li, Chaoqian; Chen, Zhen; Li, Yaotang^*

来源：Linear Algebra and Its Applications, 2015, 481: 36-53.

DOI：10.1016/j.laa.2015.04.023

• Tensor eigenvalue
• Nonnegative tensors
• Strong M-tensors
• Positive definite

A new tensor eigenvalue inclusion set is given, and proved to be tighter than those in L.Q. Qi (2005) [18] and C.Q. Li, Y.T. Li, X. Kong (2014) [12]. In addition, we study the eigenvalues lying on the boundary of the eigenvalue inclusion set provided by Qi (2005) for weakly irreducible tensors. As applications, we give new bounds for the spectral radius of nonnegative tensors, some sufficient conditions for a tensor to be a strong M-tensor and some inequalities to identify the positive definiteness for an even-order real supersymmetric tensor.

• 出版日期2015-9-15
• 单位贵州师范大学; 北京计算科学研究中心; 云南大学