  It is well-known that the exceptional Lie algebras $\mathfrak{f}_4$ and
$\mathfrak{g}_2$ arise from the octonions as the derivation algebras of the
$3\times3$ hermitian and $1\times1$ antihermitian matrices, respectively.
Inspired by this, we compute the derivation algebras of the spaces of hermitian
and antihermitian matrices over an octonion algebra in all dimensions.
