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The characteristic polynomial 
${{P}_{A}}({{x}_{0}},...,{{x}_{r}})$ of an 
$r$-tuple 
$A\,:=({{A}_{1}},...,{{A}_{r}})$ of 
$n\times n$-matrices is defined as
1
$${{P}_{A}}({{x}_{0}},...,{{x}_{r}}):=\det ({{x}_{0}}I+{{x}_{1}}{{A}_{1}}+\ldots +{{x}_{r}}{{A}_{r}}).$$
We show that if 
$r\,\,3$ and $A\,:=({{A}_{1}},...,{{A}_{r}})$ is an $r$-tuple of $n\times n$-matrices in general position, then up to conjugacy, there are only finitely many $r$-tuples 
$A'\,:=(A_{1}^{'},...,A_{r}^{'})$ such that 
${{p}_{A}}={{p}_{A'}}$. Equivalently, the locus of determinantal hypersurfaces of degree 
$n$ in 
${{\text{P}}^{r}}$ is irreducible of dimension 
$(r-1){{n}^{2}}+1$.
