I can't seem to derive this results that my book "Linear Algebra Done right" is using without explanation. It must be obvious but I don't see it.
Let $T$ be a self adjoint operator. How do they go from $ \langle T^2(v), v\rangle = \langle Tv, Tv\rangle $ I know $T^2=T^*T $ however I still don't see the jump from $\langle T^*T(v),v\rangle $ to $\langle Tv,Tv\rangle $
Also usually when I read questions/answers with operators and the like they mention Hilbert spaces, but I haven't learned about those at all.