Inertia of the stein transformation with respect to some nonderogatory matrices

Autor: Luz Maria DeAlba
Rok vydání: 1996
Předmět:
Zdroj: Linear Algebra and its Applications. :191-201
ISSN: 0024-3795
DOI: 10.1016/0024-3795(95)00546-3
Popis: Let A be an n-by-n nonderogatory matrix all of whose eigenvalues lie on the unit circle, and let π and ν be nonnegative integers with π + ν = n. Let π′ and ν′ be positive integers and δ′ a nonnegative integer with π′ + ν′ + δ′ = n. In this paper we explore the existence of a Hermitian nonsingular matrix K with inertia (π, ν, 0), such that the Stein transformation of K corresponding to A, SA(K) = K − AKA∗, is a Hermitian matrix with inertia (π′, ν′, δ′). The study is done by reducing A to Jordan canonical form. If C is an n-by-n nonderogatory matrix all of whose eigenvalues lie on the imaginary axis, then the results obtained for SA(K) are valid for the Lyapunov transformation, LC(K) = CK + KC∗, of K corresponding to C.
Databáze: OpenAIRE