Matrices are often used for doing transformations, especially when a large number of points are being transformed, as they are a direct representation of the linear operator. Rotations represented in other ways are often converted to matrices before being used. They can be extended to represent rotations and transformations at the same time using homogeneous coordinates. Projective transformations are represented by matrices. They are not rotation matrices, but a transformation that represents a Euclidean rotation has a rotation matrix in the upper left corner.