# "Inertia of the stein transformation with respect to some nonderogatory matrices"

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## Authors

DeAlba, Luz M.

## Issue Date

1996-07

## Type

Article

## Language

en_US

## Keywords

Inertia , Stein transformation , Nonderogatory matrices , Algebra

## Alternative Title

## Abstract

Let A be an n-by-n nonderogatory matrix all of whose eigenvalues lie on the unit circle, and let and be nonnegative integers with + = n. Let ′ and ′ be positive integers and ′ a nonnegative integer with ′ + ′ + ′ = n. In this paper we explore the existence of a Hermitian nonsingular matrix K with inertia ( , , 0), such that the Stein transformation of K corresponding to A, SA(K) = K − AKA*, is a Hermitian matrix with inertia ( ′, ′, ′). 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.

## Description

Proceedings of the Fourth Conference of the International Linear Algebra Society.

## Citation

LINEAR ALGEBRA AND ITS APPLICATIONS, July-August 1996, Pages 191-201.

## Publisher

Elsevier Science

## License

## Journal

## Volume

## Issue

## PubMed ID

## DOI

## ISSN

0024-3795