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New Brualdi-type eigenvalue inclusion sets for tensors. (English) Zbl 1458.15024

Summary: In this paper, two Brualdi-type eigenvalue inclusion sets are presented, which are characterized by the girth of the digraph associated with a tensor and are proved weaker than the conditions of Brualdi-type eigenvalue inclusion sets given by C. Bu et al. [Linear Algebra Appl. 480, 168–175 (2015; Zbl 1320.15019)]. As applications of the above results, the conditions of nonsingularity and positive definiteness of tensors are given.

MSC:

15A18 Eigenvalues, singular values, and eigenvectors
15A69 Multilinear algebra, tensor calculus

Citations:

Zbl 1320.15019
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References:

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