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Variational characterizations of the sign-real and the sign-complex spectral radius
Publikationstyp
Journal Article
Date Issued
2002
Sprache
English
Author(s)
Institut
TORE-URI
Volume
9
Start Page
112
End Page
117
Citation
Electronic Journal of Linear Algebra 9: 112-117 (2002)
Publisher DOI
Scopus ID
Publisher
ILAS, The International Linear Algebra Society
The sign-real and the sign-complex spectral radius, also called the generalized spectral radius, proved to be an interesting generalization of the classical Perron-Frobenius theory (for nonnegative matrices) to general real and to general complex matrices, respectively. Especially the generalization of the well-known Collatz-Wielandt max-min characterization shows one of the many one-to-one correspondences to classical Perron-Frobenius theory. In this paper the corresponding inf-max characterization as well as variational characterizations of the generalized (real and complex) spectral radius are presented. Again those are almost identical to the corresponding results in classical Perron-Frobenius theory.
Subjects
Generalized spectral radius
Perron-Frobenius theory
Sign-complex spectral radius
Sign-real spectral radius
DDC Class
510: Mathematik