Difference between revisions of "Template:Reflection matrix"
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| − | 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 | + | 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>). |
Latest revision as of 19:55, 5 March 2018
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 unitary (U^{*}U=E) and Hermitian (U^{*}=U) at the same time; consequently, this matrix is its own inverse (U^{-1}=U).
