I have come across a statement in my book, that doesn't seem obvious to me.
Lets say i have an orthonormal basis $z = {z_1,z_2}$ for a subspace $V$ and a another set of vectors $q = {q_1, q_2} $ thats the orthonormal basis for the complement $V^⊥$ of $V$.
How might i express a vector $e_1$ as $e_1 = z + q$ where $q \in V^⊥$, $z \in V$.
EDIT: The question is then how can one fine $e_1$?