I'm trying to solve the following problem with the orthogonality principle:
$$ \pmb x^*= \text{argmin}\;\; \pmb x^H Q \pmb x \quad s.t. \quad A\pmb x = \pmb b $$
I think I'll get something that looks like $QA^H(AQA^H)^{-1}$ but I keep getting stuck because the constraint isn't written in terms of the inner product defined by $\langle \pmb x, \pmb y\rangle = \pmb y^H Q \pmb x$