On a matrix associated to a matrix pair

Abstract

AbstractFor a c–stable matrix pair (E,A), i.e., all finite eigenvalues of (E,A) have negative real part, an associated c–stable matrix is provided. It has all finite eigenvalues of (E,A) as eigenvalues and an additional stable eigenvalue −α, where α may be chosen arbitrarily, which corresponds to the eigenvalue ∞ of (E,A). In the case of positive systems, this associated c–stable matrix is, in addition, shown to be a −M‐matrix. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)