Pseudoreflection

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This article is about one meaning of the term "pseudoreflection". For another meaning, see complex reflection group.

In mathematics, a pseudoreflection is a transformation of the form

\begin{bmatrix}
  1      & \cdots & 0      \\
  \vdots & \ddots & \vdots \\ 
  0      & \cdots & -1
\end{bmatrix}

with all but one of the diagonal elements 1. If the space on which this transformation acts has a symmetric bilinear form defined on it, so that vectors can be orthogonal, then the transformation is a true reflection.