Volume 51, pp. 262-273, 2019.

${}_{\delta}^{\gamma}\!\mathbf{\Phi}$-type inclusion set for eigenvalues of a tensor

Xiao-Qiang Lei


In this paper, a new ${}_{\delta}^{\gamma}\!\mathbf{\Phi}$-type eigenvalue inclusion set for tensors is given, and some inclusion relations between this new inclusion set and other ones are presented. In addition, a new sufficient criterion for identifying nonsingular tensors is also provided by using the new ${}_{\delta}^{\gamma}\!\mathbf{\Phi}$-type eigenvalue inclusion set. Some numerical results are reported to show the superiority of the results.

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Key words

tensor, eigenvalue, inclusion, nonsingular, ${}_{\delta}^{\gamma}\!\mathbf{\Phi}$-type.

AMS subject classifications

15A69, 15A18, 65F15, 65H17, 15A15, 65F40

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