Inertia of the stein transformation with respect to some nonderogatory matrices
Autor: | Luz Maria DeAlba |
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Rok vydání: | 1996 |
Předmět: |
Numerical Analysis
Pure mathematics Algebra and Number Theory Mathematical analysis Hermitian matrix law.invention Matrix (mathematics) Transformation (function) Invertible matrix Unit circle Integer law Discrete Mathematics and Combinatorics Canonical form Geometry and Topology Eigenvalues and eigenvectors Mathematics |
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 |
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