Abstract
The real rectangular tensors arise from the strong ellipticity condition problem in solid mechanics and the entanglement problem in quantum physics. In this paper, we study the singular values/vectors problem of real nonnegative partially symmetric rectangular tensors. We first introduce the concepts of lk,s-singular values/vectors of real partially symmetric rectangular tensors. Then, based upon the presented properties of lk,s-singular values /vectors, some properties of the related lk,s-spectral radius are discussed. Furthermore, we prove two analogs of Perron-Frobenius theorem and weak Perron-Frobenius theorem for real nonnegative partially symmetric rectangular tensors.
| Original language | English |
|---|---|
| Pages (from-to) | 63-83 |
| Number of pages | 21 |
| Journal | Frontiers of Mathematics in China |
| Volume | 8 |
| Issue number | 1 |
| DOIs | |
| Publication status | Published - 14 Jan 2013 |
Keywords
- irreducibility
- l -singular value k,s
- l -spectral radius k,s
- Nonnegative rectangular tensor
- weak irreducibility
ASJC Scopus subject areas
- Mathematics (miscellaneous)