Linear Algebra Done Right
《Linear Algebra Done Right》 · 第 214 页 · Section 6C「Orthogonal Projections and Minimization Problems」，Definition 6.55
Suppose $U$ is a finite-dimensional subspace of $V$. The orthogonal projection of $V$ onto $U$ is the operator $P_U\in\mathcal L(V)$ defined as follows: For each $v\in V$, write $v=u+w$, where $u\in U$ and $w\in U^\perp$. Then let $P_Uv=u$.