%0 Journal Article
%T The higher rank numerical range of matrix polynomials
%A Aikaterini Aretaki
%A John Maroulas
%J Mathematics
%D 2011
%I arXiv
%X The notion of the higher rank numerical range $\Lambda_{k}(L(\lambda))$ for matrix polynomials $L(\lambda)=A_{m}\lambda^{m}+...+A_{1}\lambda+A_{0}$ is introduced here and some fundamental geometrical properties are investigated. Further, the sharp points of $\Lambda_{k}(L(\lambda))$ are defined and their relation to the numerical range $w(L(\lambda))$ is presented. A connection of $\Lambda_{k}(L(\lambda))$ with the vector-valued higher rank numerical range $\Lambda_{k}(A_{0},..., A_{m})$ is also discussed.
%U http://arxiv.org/abs/1104.1341v1