Allow problems concerning spectral properties of sign pattern matrices: A survey
| Autor: | Minerva Catral, P. van den Driessche, Dale D. Olesky |
|---|---|
| Rok vydání: | 2009 |
| Předmět: |
Signed digraph
0211 other engineering and technologies Potentially stable 010103 numerical & computational mathematics 02 engineering and technology 01 natural sciences Stability (probability) Square matrix Combinatorics Matrix (mathematics) Discrete Mathematics and Combinatorics Potentially nilpotent 0101 mathematics Inertially arbitrary Mathematics Numerical Analysis Algebra and Number Theory 021107 urban & regional planning Digraph Graph theory Nilpotent Sign pattern matrix Geometry and Topology Nilpotent group Spectrally arbitrary Sign (mathematics) |
| Zdroj: | Linear Algebra and its Applications. 430(11-12):3080-3094 |
| ISSN: | 0024-3795 |
| DOI: | 10.1016/j.laa.2009.01.031 |
| Popis: | An n × n sign pattern matrix has entries in { + , - , 0 } . This paper surveys the following problems concerning spectral properties of sign pattern matrices: sign patterns that allow all possible spectra (spectrally arbitrary sign patterns); sign patterns that allow all inertias (inertially arbitrary sign patterns); sign patterns that allow nilpotency (potentially nilpotent sign patterns); and sign patterns that allow stability (potentially stable sign patterns). Relationships between these four classes of sign patterns are given, and several open problems are identified. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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