Let $T$ be a complex linear representation of the group $G$ in a space $V$
Show that $\dim V^{G} = 1/|G| \sum_{g \in G} \chi_{T} (g).$
If I know the definition of $V^G$ from this corollary:
Which means like the elements of $V_{k}$ on which $T_{k}(h)$ is the trivial representation for all $h \in H.$
And we know the definition of $\chi_{T}$ from the following corollary:
But then I can not see how the $\dim V^G$ will be equal this, could anyone explain this for me please?