Pseudoreflection

In mathematics, a pseudoreflection is an invertible linear transformation of a finite-dimensional vector space such that it is not the identity transformation, has a finite (multiplicative) order, and fixes a hyperplane. The concept of pseudoreflection generalizes the concepts of reflection and complex reflection and is simply called reflection by some mathematicians. It plays an important role in Invariant theory of finite groups, including the Chevalley-Shephard-Todd theorem.