Abstract
Matrix logarithmic norm is an important quantity, which characterize the stability of linear dynamical systems. We propose the logarithmic norms for tensors and tensor pairs, and extend some classical results from the matrix case. Moreover, the explicit forms of several tensor logarithmic norms and semi-norms are also derived. Employing the tensor logarithmic norms, we bound the real parts of all the eigenvalues of a complex tensor and study the stability of a class of nonlinear dynamical systems.
| Original language | English |
|---|---|
| Pages (from-to) | 989-1006 |
| Number of pages | 18 |
| Journal | Numerical Linear Algebra with Applications |
| Volume | 23 |
| Issue number | 6 |
| DOIs | |
| Publication status | Published - 1 Dec 2016 |
Scopus Subject Areas
- Algebra and Number Theory
- Applied Mathematics
User-Defined Keywords
- logarithmic norm
- spectral abscissa
- stability of dynamical systems
- tensor eigenvalue
- tensor norm
- tensor pair