Projection

In linear algebra, a projection is a linear map $P$ form a vector space to itself (an endomorphism) such that $P^2=P$.

Projection matrix

A square matrix $P$ is called a projection matrix if it is equal to its square

Orthogonal Projection

For example, the function which maps the point $(x,y,z)$ in 3-d space to the point $(x,y,0)$ is an orthogonal projection onto the $xy$-plane, whose matrix:

$$P=\left(\begin{array}{ccc}1& 0& 0\\ 0& 1& 0\\ 0& 0& 0\end{array}\right)$$

is a projection matrix

Oblique Projection

Like

$$P=\left(\begin{array}{cc}0& 0\\ \alpha & 1\end{array}\right)$$