- 1,723

- 51

I've been reading and it appears that the orthogonal projection of a vector ##v## to the subspace spanned by ##e_1,...,e_n## is given by $$\sum_j\langle e_j,v \rangle e_j$$ (##e_j## are unit vectors, so ignore the usual inner product denominator for simplicity) but there is never a proof in the texts. It's always given by definition or I see "trivial" next to the proof. Surely this is something we prove, right?