  A subset $\left\{x_{1},x_{2},\hdots,x_{d}\right\}$ of a group $G$
\emph{invariably generates} $G$ if
$\left\{x_{1}^{g_{1}},x_{2}^{g_{2}},\hdots,x_{d}^{g_{d}}\right\}$ generates $G$
for every $d$-tuple $(g_{1},g_{2}\hdots,g_{d})\in G^{d}$. We prove that a
finite completely reducible linear group of dimension $n$ can be invariably
generated by $\left\lfloor \frac{3n}{2}\right\rfloor$ elements. We also prove
tighter bounds when the field in question has order $2$ or $3$. Finally, we
prove that a transitive [respectively primitive] permutation group of degree
$n\geq 2$ [resp. $n\geq 3$] can be invariably generated by
$O\left(\frac{n}{\sqrt{\log{n}}}\right)$ [resp.
$O\left(\frac{\log{n}}{\sqrt{\log{\log{n}}}}\right)$] elements.
