The non-invertible linear transformations T : R → R are usually
called collapsing linear transformations.
They collapse R into a line or a point.
We say that v is projected onto p on a line through the origin if
(v − p) ⊥ p. The corresponding matrix is called a projection
If T : R → R is rotation of the plane counterclockwise through an
angl θ, then th standard matrix representation of T is
A = .
sinθ cosθ n n
Deﬁnition: Let S be a subset of R and let