Definition:Projection (Analytic Geometry)

This page is about projections in analytic geometry. For other uses, see Definition:Projection.

Definition

Let $M$ and $N$ be distinct lines through the origin in the plane.

The projection on $M$ along $N$ is the mapping $\operatorname{pr}_{M, N}$ such that:

$\forall x \in \R^2: \operatorname{pr}_{M, N} \left({x}\right) =$ the intersection of $M$ with the line through $x$ parallel to $N$.

Sources

• Seth Warner: Modern Algebra (1965): $\S 28$: Example $28.5$