Publisher DOI: 10.13001/1081-3810.1077
Title: Variational characterizations of the sign-real and the sign-complex spectral radius
Language: English
Authors: Rump, Siegfried M.  
Keywords: Generalized spectral radius;Perron-Frobenius theory;Sign-complex spectral radius;Sign-real spectral radius
Issue Date: 1-Jan-2002
Publisher: ILAS, The International Linear Algebra Society
Source: Electronic Journal of Linear Algebra 9 (): 112-117 (2002)
Journal or Series Name: The electronic journal of linear algebra 
Abstract (english): 
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.
URI: http://hdl.handle.net/11420/9421
ISSN: 1081-3810
Institute: Zuverlässiges Rechnen E-19 
Document Type: Article
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