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.