In a finite-dimensional inner-product space, $V=W\oplus W^\perp$. Choose an orthonormal basis of $W$ and extend it to an orthonormal basis of $V$; the added vectors span $W^\perp$. The intersection is zero because a vector orthogonal to itself has zero norm. Infinite-dimensional versions require additional hypotheses.
Parents
Like how this is organised?
Build your own knowledge tree on knowen.md: notes, decisions and tasks in one connected markdown graph, shared with your team and your AI agents.