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#### Article Title

On the rank-k numerical range of matrices polynomials

#### Keywords

rank-k numerical range, matrix polynomials, quantum error correc- tion

#### Abstract

This article introduces the notion of the rank-$k$ numerical range $\Lambda_{k}(L)$ of a matrix polynomial $L(\lambda) = A_{m} \lambda^{m} + \cdots + A_{1} \lambda + A_{0}$, whose coefficients are $n\times n$ complex matrices. Also, geometric properties are obtained, including the relation to the ordinary numerical range $W(L)$.

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