Template:Reflection matrix

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