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 | + | 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 [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]).
