  Let $\mathbb{F}$ be a field and $f : \mathfrak{S}_n \rightarrow \mathbb{F}
\setminus \{0\}$ be an arbitrary map. The Schur matrix functional associated to
$f$ is defined as $M \in \text{M}_n(\mathbb{F}) \mapsto
\widetilde{f}(M):=\sum_{\sigma \in \mathfrak{S}_n} f(\sigma) \prod_{j=1}^n
m_{\sigma(j),j}$. Typical examples of such functionals are the determinant
(where $f$ is the signature morphism) and the permanent (where $f$ is constant
with value $1$). Given two such maps $f$ and $g$, we study the endomorphisms
$U$ of the vector space $\text{M}_n(\mathbb{F})$ that satisfy
$\widetilde{g}(U(M))=\widetilde{f}(M)$ for all $M \in \text{M}_n(\mathbb{F})$.
In particular, we give a closed form for the linear preservers of the
functional $\widetilde{f}$ when $f$ is central, and as a special case we extend
to an arbitrary field Botta's characterization of the linear preservers of the
permanent.
