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| In [[Linear algebra]], define the '''Householder operator''' as follows.
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| Let <math> V\, </math> be a finite dimensional [[inner product space]] with [[unit vector]] <math> u\in V</math> Then, the Householder operator is an [[Operator (mathematics)|operator]] <math> H_u : V \to V\,</math> defined by
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| :<math> H_u(x) = x - 2\langle x,u \rangle u\,</math>
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| where <math> \langle \cdot, \cdot \rangle </math> is the [[inner product]] over <math>V\,</math>. This operator reflects the vector <math>x</math> across a plane given by the normal vector <math>u</math>.<ref>{{cite book|title=Methods of Applied Mathematics for Engineers and Scientist|publisher=Cambridge University Press|isbn=9781107244467|pages=Section E.4.11|url=http://books.google.com/books?id=nQIlAAAAQBAJ}}</ref>
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| Over a [[real vector space]], the Householder operator is also known as the [[Householder transformation]].
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| The Householder operator has numerous properties such as linearity, being [[self-adjoint]], and is a [[Unitary operator|unitary]] or [[orthogonal]] operator on V.
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| ==References==
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| {{reflist}}
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| [[Category:Numerical linear algebra]]
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| {{Linear-algebra-stub}}
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Latest revision as of 19:29, 13 April 2014
Hello. Allow me introduce the author. Her name is Emilia Shroyer but it's not the most female name out there. Doing ceramics is what my family members and I enjoy. My day job is a meter reader. For a whilst she's been in South Dakota.
my web-site ... std home test