ELA, Volume 9, pp. 112-117, June 2002, abstract.

Variational Characterizations of the Sign-Real 
and the Sign-Complex Spectral Radius

Siegfried M. Rump

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.