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|Author||DeAlba, Luz M.|
|Date of Issue||1996-07|
|Identifier (Citation)||LINEAR ALGEBRA AND ITS APPLICATIONS, July-August 1996, Pages 191-201.||en|
|Description||Proceedings of the Fourth Conference of the International Linear Algebra Society.||en|
|Description||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.||en|
|Sponsorship||Partially supported by a Drake University Faculty Research Grant.||en|
|Title||"Inertia of the stein transformation with respect to some nonderogatory matrices"||en|
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Mathematics and Computer Science
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