Linear preservers of polynomial numerical hulls of matrices
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Date
2019-08-15
Authors
Aghamollaei, Gh.
Marcoux, L.W.
Radjavi, H.
Advisor
Journal Title
Journal ISSN
Volume Title
Publisher
Elsevier
Abstract
Let Mn be the algebra of all n × n complex matrices, 1 ≤ k ≤ n − 1 be an integer, and φ : Mn −→ Mn be a linear operator. In this paper, it is shown that φ preserves the polynomial numerical hull of order k if and only if there exists a unitary matrix U ∈ Mn such that either φ(A)=U∗AU forallA∈Mn,orφ(A)=U∗AtU forallA∈Mn.
Description
The final publication is available at Elsevier via https://doi.org/10.1016/j.laa.2019.03.029. © 2019. This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/
Keywords
linear preserver, polynomial numerical hull, numerical range