Abstract
By combinatorial and matrix theoretical methods, the study is focused on some special sign pattern matrices. A class of spectrally and inertially arbitrary zero-nonzero pattern is given. It is proved that the Hessenberg-matrix is the minimal inertially arbitrary sign pattern. An almost inertially arbitrary sign pattern that is constructed by the direct sum from those of lower order is introduced. Based on the property of matrix-decomposition for analyzing S-shaped sign pattern matrix, a necessary condition on the spectrally arbitrary sign pattern matrix is characterized.
| Original language | English |
|---|---|
| Pages (from-to) | 307-311 |
| Number of pages | 5 |
| Journal | Zhongbei Daxue Xuebao (Ziran Kexue Ban)/Journal of North University of China (Natural Science Edition) |
| Volume | 30 |
| Issue number | 4 |
| State | Published - Aug 2009 |
| Externally published | Yes |
Keywords
- Almost inertially arbitrary
- Inertia arbitrary
- Minimal spectrally arbitrary pattern
- Sign pattern
- Spectral arbitrary