Source: cirosantilli/lie-algebra-of-gl-n
= Lie algebra of $GL(n)$
{c}
{tag=Lie algebra of a matrix Lie group}
Is the <set of all n-by-y square matrices>.
Because <GL(n)> is a <Lie group> we can use <Lie algebra of a matrix Lie group>{full}.
For every matrix $x$ in the <set of all n-by-y square matrices> $M_n$, $e^x$ has inverse $e^-x$.
Note that this works even if $x$ is not <invertible>, and therefore not in <GL(n)>!
Therefore, the Lie algebra of <GL(n)> is the entire <M_n>.