  We prove an explicit formula for the invariant $\mu(\Lg)$ for
finite-dimensional semisimple, and reductive Lie algebras $\Lg$ over $\C$. Here
$\mu(\Lg)$ is the minimal dimension of a faithful linear representation of
$\Lg$. The result can be used to study Dynkin's classification of maximal
reductive subalgebras of semisimple Lie algebras.
