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In linear algebra, the Crout matrix decomposition is an LU decomposition which decomposes a matrix into a lower triangular matrix (L), an upper triangular matrix (U) and, although not always needed, a permutation matrix (P). It was developed by Prescott Durand Crout. The Crout matrix decomposition algorithm differs slightly from the Doolittle method. Doolittle's method returns a unit lower triangular matrix and an upper triangular matrix, while the Crout method returns a lower triangular matrix and a unit upper triangular matrix. So, if a matrix decomposition of a matrix A is such that: A = LDU

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rdf:type	yago:WikicatMatrixDecompositions yago:Abstraction100002137 yago:Algebra106012726 yago:Cognition100023271 yago:Content105809192 yago:Decomposition106013471 yago:Discipline105996646 yago:KnowledgeDomain105999266 yago:Mathematics106000644 yago:PsychologicalFeature100023100 yago:PureMathematics106003682 yago:Science105999797 yago:VectorAlgebra106013298
rdfs:label	Crout matrix decomposition (en) Crout-decompositie (nl)
rdfs:comment	De Crout-decompositie is een algoritme voor de LU-decompositie van een vierkante niet-singuliere matrix in een benedendriehoeksmatrix en een bovendriehoeksmatrix In de matrix zijn de elementen op de hoofddiagonaal gelijk aan 1. De methode is genoemd naar , wiskundige aan het Massachusetts Institute of Technology die ze in 1941 beschreef. (nl) In linear algebra, the Crout matrix decomposition is an LU decomposition which decomposes a matrix into a lower triangular matrix (L), an upper triangular matrix (U) and, although not always needed, a permutation matrix (P). It was developed by Prescott Durand Crout. The Crout matrix decomposition algorithm differs slightly from the Doolittle method. Doolittle's method returns a unit lower triangular matrix and an upper triangular matrix, while the Crout method returns a lower triangular matrix and a unit upper triangular matrix. So, if a matrix decomposition of a matrix A is such that: A = LDU (en)
dct:subject	Matrix decompositions
Wikipage page ID	900131 (xsd:integer)
Wikipage revision ID	956132782 (xsd:integer)
Link from a Wikipage to another Wikipage	Algorithm Permutation matrix Matrix (mathematics) LU decomposition Linear algebra Prescott Durand Crout Matrix decompositions Upper triangular matrix Doolittle decomposition Lower triangular matrix
Link from a Wikipage to an external page	https://web.archive.org/web/20131003135132/http:/tutorialfrenzy.com/matlab-crout-lu-factorization-linear-equations-systems.php
sameAs	Crout matrix decomposition Crout matrix decomposition Crout matrix decomposition Crout matrix decomposition Crout matrix decomposition Crout matrix decomposition
dbp:wikiPageUsesTemplate	dbt:Reflist
has abstract	In linear algebra, the Crout matrix decomposition is an LU decomposition which decomposes a matrix into a lower triangular matrix (L), an upper triangular matrix (U) and, although not always needed, a permutation matrix (P). It was developed by Prescott Durand Crout. The Crout matrix decomposition algorithm differs slightly from the Doolittle method. Doolittle's method returns a unit lower triangular matrix and an upper triangular matrix, while the Crout method returns a lower triangular matrix and a unit upper triangular matrix. So, if a matrix decomposition of a matrix A is such that: A = LDU being L a unit lower triangular matrix, D a diagonal matrix and U a unit upper triangular matrix, then Doolittle's method produces A = L(DU) and Crout's method produces A = (LD)U. (en) De Crout-decompositie is een algoritme voor de LU-decompositie van een vierkante niet-singuliere matrix in een benedendriehoeksmatrix en een bovendriehoeksmatrix In de matrix zijn de elementen op de hoofddiagonaal gelijk aan 1. De methode is genoemd naar , wiskundige aan het Massachusetts Institute of Technology die ze in 1941 beschreef. (nl)
gold:hypernym	Decomposition
prov:wasDerivedFrom	wikipedia-en:Crout_matrix_decomposition?oldid=956132782&ns=0
page length (characters) of wiki page	2638 (xsd:nonNegativeInteger)
foaf:isPrimaryTopicOf	wikipedia-en:Crout_matrix_decomposition
is Link from a Wikipage to another Wikipage of	List of numerical analysis topics LU decomposition Crout Prescott Durand Crout Crout's Method Crout's algorithm Crout's method Crout decomposition
is Wikipage redirect of	Crout's Method Crout's algorithm Crout's method Crout decomposition
is Wikipage disambiguates of	Crout
is foaf:primaryTopic of	wikipedia-en:Crout_matrix_decomposition

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