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| "A '''block reflector''' is an orthogonal, symmetric [[matrix (mathematics)|matrix]] that reverses a subspace whose dimension may be greater than one."
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| * see abstract here http://locus.siam.org/SINUM/volume-25/art_0725014.html
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| It is built out of many [[elementary reflector]]s.
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| It is also referred to as a [[triangular factor]], and is a [[triangular matrix]] and they are used in the [[Householder transformation]].
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| A reflector <math> Q </math> belonging to <math>\mathcal M_n(\R) </math> can be written in the form :
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| <math> Q = I -auu^T </math> where <math>I</math> is the [[identity matrix]] for <math>\mathcal M_n(\R) </math> , <math>a</math> is a [[Scalar (mathematics)|scalar]] and <math>u</math> belongs to <math>\mathcal \R^n </math> .
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| ==LAPACK routines==
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| Here are some of the [[LAPACK]] routines that apply to block reflectors
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| * "*larft" forms the triangular vector T of a block reflector H=I-VTVH.
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| * "*larzb" applies a block reflector or its [[transpose]]/[[conjugate transpose]] as returned by "*tzrzf" to a general [[matrix (mathematics)|matrix]].
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| * "*larzt" forms the triangular vector T of a block reflector H=I-VTVH as returned by "*tzrzf".
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| * "*larfb" applies a block reflector or its [[transpose]]/[[conjugate transpose]] to a general rectangular matrix.
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| ==See also==
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| * [[Reflection (mathematics)]]
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| * [[Householder transformation]]
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| * [[Unitary matrix]]
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| * [[Triangular matrix]]
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| [[Category:Matrices]]
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| {{Linear-algebra-stub}}
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| {{compu-prog-stub}}
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Latest revision as of 12:10, 15 April 2014
Oscar is what my wife enjoys to call me and I completely dig that title. I am a meter reader but I strategy on altering it. South Dakota is exactly where me and my husband live. One of the things she enjoys most is to do aerobics and now she is trying to make cash with it.
Also visit my blog post https://Tomjones1190.Wordpress.com/