Orthogonal projection

Orthogonal projection

For example, the function which maps the point ${\displaystyle (x,y,z)}$ in three-dimensional space ${\displaystyle \mathbb {R} ^{3}}$ to the point ${\displaystyle (x,y,0)}$ is an orthogonal projection onto the xy-plane. This function is represented by the matrix $${\displaystyle P={\begin{bmatrix}1&0&0\\0&1&0\\0&0&0\end{bmatrix}}.}$$