Editing Transformation matrix (section)

===Orthogonal projection===
{{further|Orthogonal projection}}

To project a vector orthogonally onto a line that goes through the origin, let <math>\mathbf{u} = (u_x, u_y)</math> be a [[vector (geometric)|vector]] in the direction of the line.  Then the transformation matrix is:
<math display="block">\mathbf{A} = \frac{1}{\lVert\mathbf{u}\rVert^2} \begin{bmatrix} u_x^2 & u_x u_y \\ u_x u_y & u_y^2 \end{bmatrix}</math>

As with reflections, the orthogonal projection onto a line that does not pass through the origin is an affine, not linear, transformation.

[[Projection (linear algebra)|Parallel projections]] are also linear transformations and can be represented simply by a matrix.  However, perspective projections are not, and to represent these with a matrix, [[Homogeneous coordinates#Use in computer graphics and computer vision|homogeneous coordinates]] can be used.