In a finite-dimensional real inner product space, a reflection is a linear transformation that fixes a linear hyperplane pointwise and negates the vector orthogonal to the plane. This notion may be extended to vector spaces over other fields. In particular, in a complex inner product space, a reflection is a unitary transformation T of finite order that fixes a hyperplane. This implies that the vectors orthogonal to the hyperplane are eigenvectors of T, and the associated eigenvalue is a complex root of unity. A complex reflection group is a finite group of linear transformations on a complex vector space generated by reflections.