Template:Reflection matrix

A reflection (or a Householder) matrix is a matrix of the form $U=E-2ww^*$, where the vector $w$ is normalized: $w^{*}w=1$. Such a matrix is at the same time unitary ($U^{*}U=E$) and Hermitian ($U^{*}=U$); consequently, this matrix is its own inverse ($U^{-1}=U$).