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Householder transformation

In linear algebra, a Householder transformation (also known as a Householder reflection or elementary reflector) is a linear transformation that describes a reflection about a plane or hyperplane containing the origin. The Householder transformation was used in a 1958 paper by Alston Scott Householder.

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Definition

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Computational and theoretical relationship to other unitary transformations

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Householder transformation

Nodes54
Edges53
Triples53
Avg. degree1.96
Density0.037037
Components1

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Householder transformation

Top relations

related to References · 46
Householder transformation → ACM, Advanced Linear Algebra, Algorithms, American Mathematical Society, Archived, Barry, BP, Cambridge University Press, Century, Cipra, Computation, Editors Name Top, Flannery, Graduate Texts, Herein Householder Transformation, Householder Method, ISBN, Journal, JSTOR, LaBudde
related to Computational and theoretical relationship to other unitary transformations · 6
Householder transformation → An, Since, Taking, The Householder, This, UU
is a · 1
Householder transformation → reflection about a hyperplane with unit normal vector v

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Important terminology

displaystyle householder matrix transformation vector vec unitary hermitian textstyle matrices since real alpha also transformations similarity linear text used reflection

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SubjectPredicateObjectConfidenceSrc
Householder transformationis areflection about a hyperplane with unit normal vector v0.90text
Householder transformationrelated to Computational and theoretical relationship to other unitary transformationsThe Householder0.60section
Householder transformationrelated to Computational and theoretical relationship to other unitary transformationsAn0.60section
Householder transformationrelated to Computational and theoretical relationship to other unitary transformationsUU0.60section
Householder transformationrelated to Computational and theoretical relationship to other unitary transformationsTaking0.60section
Householder transformationrelated to Computational and theoretical relationship to other unitary transformationsThis0.60section
Householder transformationrelated to Computational and theoretical relationship to other unitary transformationsSince0.60section
Householder transformationrelated to ReferencesLaBudde0.60section
Householder transformationrelated to ReferencesThe0.60section
Householder transformationrelated to ReferencesMathematics0.60section
Householder transformationrelated to ReferencesComputation0.60section
Householder transformationrelated to ReferencesAmerican Mathematical Society0.60section

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