Aghamollaei, Gh.Marcoux, L.W.Radjavi, H.2020-04-012020-04-012019-08-15https://doi.org/10.1016/j.laa.2019.03.029http://hdl.handle.net/10012/15728The 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/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.enAttribution-NonCommercial-NoDerivatives 4.0 Internationallinear preserverpolynomial numerical hullnumerical rangeArticle