# [Math] Why is it called “Orthogonal Projection”? Why not just “Projection”

linear algebra

Right now, we are learning decomposing vectors, but something I don't understand is the names given to this stuff

For instance, in the text, the parallel component of y is said to be the orthogonal projection of y onto u. This makes no sense to me. Why is the word "orthogonal" even in there in the first place? I think I understand why they use "orthogonal" for z, but it makes no sense to me when they could just call it "orthogonal"

If $p:V\to W$ is an $\color{Green}{orthogonal}$ projection down to a subspace, the fibers (pre-images) of every point $w\in W$ is perpendicular to the base (the subspace $W$). With $\dim V=2$ and $\dim W=1$:
$\hskip 0.4in$