It is shown that vertex stability implies Schur D-stability for real 3 ร 3 matrices. Also, principally nilpotent n ร n complex matrices are shown to be perfectly Schur D -stable, and additional characterizations of these matrices are given.
Characterizations of classes of stable matrices
โ Scribed by A. Bhaya; E. Kaszkurewicz; R. Santos
- Publisher
- Elsevier Science
- Year
- 2003
- Tongue
- English
- Weight
- 154 KB
- Volume
- 374
- Category
- Article
- ISSN
- 0024-3795
No coin nor oath required. For personal study only.
โฆ Synopsis
This paper extends some results on the structure of subsets of the set of stable matrices. For these subsets, different characterizations are obtained using the set product, defined in this paper, as well as inertia and algebraic characterizations for low dimensions (2ร2 and 3ร3 matrices). Some inclusion relations that hold for these classes of matrices are proved and some open questions mentioned.
๐ SIMILAR VOLUMES
In the paper we present two characterizations of classes of digraphs. The first is a forbidden triple characterization of digraphs with augmented adjacency matrices having consecutive ones property for columns. The second is a forbidden circuit characterization of digraphs with totally balanced augm