Transformations of 4-Space

Abstract

By a transformation of 4-space, we mean a rule T which assigns to each vector X of ℝ⁴ some vector T(X) of ℝ⁴. The vector T(X) is called the image of X under T, and the collection of all images of vectors in ℝ⁴ under the transformation T is called the range of T. We continue to denote transformations by capital letters such as P, Q, R, S, T.