Perron-Frobenius theory for complex matrices

Publikationstyp
Conference Paper
Date Issued
2002-12-04
Sprache
English
Author(s)
Rump, Siegfried M.  orcid-logo
Institut
Zuverlässiges Rechnen E-19  
TORE-URI
http://hdl.handle.net/11420/8728
Journal
Linear algebra and its applications  
Volume
363
Start Page
251
End Page
273
Citation
Linear Algebra and Its Applications (363): 251-273 (2003-04-01)
Publisher DOI
10.1016/S0024-3795(02)00329-4
Scopus ID
2-s2.0-84867921989
Publisher
American Elsevier Publ.
The purpose of this paper is to present a unified Perron-Frobenius Theory for nonnegative, for real not necessarily nonnegative and for general complex matrices. The sign-real spectral radius was introduced for general real matrices. This quantity was shown to share certain properties with the Perron root of nonnegative matrices. In this paper we introduce the sign-complex spectral radius. Again, this quantity extends many properties of the Perron root of nonnegative matrices to general complex matrices. Various characterizations will be given, and many open problems remain.
Subjects
μ-number
Distance to singularity
Perron-Frobenius
Unified theory
DDC Class
004: Informatik
510: Mathematik