|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|
|Appears in Collections:||Publications without fulltext|
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