A study on T-eigenvalues of third-order tensors. (English) Zbl 1458.15020
Summary: In this paper, we study T-eigenvalues of third-order tensors. Definitions of the T-eigenvalues and Hermitian tensors are proposed. We present a commutative tensor family. We prove some T-eigenvalue inequalities for Hermitian tensors, including extensions of Weyl’s theorem and Cauchy’s interlacing theorem from the matrix case to the tensor case. Finally, we introduce the stability of the T-eigenvalues and study the Lyapunov equation for tensors.
MSC:
| 15A18 | Eigenvalues, singular values, and eigenvectors |
| 15A69 | Multilinear algebra, tensor calculus |
Keywords:
T-product; T-eigenvalue; Hermitian tensor; commutative tensor family; stability; Lyapunov equationReferences:
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