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We consider rotational hypersurfaces in the $n$-dimensional Euclidean space${\mathbb{E}}^{n}$. We study the Gauss map $\mathbf{G}$ of rotationalhypersurface in ${\mathbb{E}}^{n}$ with respect to the operator $L_{k}$ actingon the functions defined on the hypersurfaces with some integers $k=n-3,$$n\geq 3$. We obtain the classification theorem with Gauss map $ \mathbf{G}$satisfying $L_{n-3}\mathbf{G}=\mathbf{AG}$ for some $n\times n$ matrix$\mathbf{A}$.

Rotational hypersurfaces satisfying $L_{n-3}\mathbf{G}=\mathbf{AG}$ in $n$-space