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A study on T-eigenvalues of third-order tensors
- Source :
- Linear Algebra and its Applications. 612:357-374
- Publication Year :
- 2021
- Publisher :
- Elsevier BV, 2021.
-
Abstract
- 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.
- Subjects :
- Numerical Analysis
Pure mathematics
Algebra and Number Theory
Cauchy distribution
Mathematics::Spectral Theory
Stability (probability)
Hermitian matrix
symbols.namesake
Matrix (mathematics)
symbols
Discrete Mathematics and Combinatorics
Lyapunov equation
Geometry and Topology
Tensor
Commutative property
Eigenvalues and eigenvectors
Mathematics
Subjects
Details
- ISSN :
- 00243795
- Volume :
- 612
- Database :
- OpenAIRE
- Journal :
- Linear Algebra and its Applications
- Accession number :
- edsair.doi...........3e5bfbc29270fc6c7929acf29ec50a33