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Statements

Subject Item
dbr:Crout_matrix_decomposition
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yago:Science105999797 yago:Algebra106012726 yago:Abstraction100002137 yago:Content105809192 yago:PureMathematics106003682 yago:Mathematics106000644 yago:Decomposition106013471 yago:VectorAlgebra106013298 yago:Cognition100023271 yago:Discipline105996646 yago:KnowledgeDomain105999266 yago:WikicatMatrixDecompositions yago:PsychologicalFeature100023100
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Crout matrix decomposition Crout-decompositie
rdfs:comment
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 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.
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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 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. 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.
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