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Elementary matrix

In mathematics, an elementary matrix is a square matrix obtained from the application of a single elementary row operation to the identity matrix. The elementary matrices generate the general linear group GLn(F) when F is a field. Left multiplication (pre-multiplication) by an elementary matrix represents the corresponding elementary row operation, while…

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Overview

MathematicsMatrixIdentity matrixGeneral linear groupField
14 related topics

Elementary row operations

Yoneda lemmaScalar
2 related topics

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Overview

Elementary row operations

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Elementary matrix

Nodes19
Edges18
Triples17
Avg. degree1.89
Density0.105263
Components1

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Elementary matrix

Top relations

related to Elementary row operations · 6
Elementary matrix → EA, If, The, There, This, Yoneda
related to Row-addition transformations · 4
Elementary matrix → And, Lij, So Lij, The
is a · 3
Elementary matrix → diagonal matrix, identity matrix but with an m in the, square matrix obtained from the application of a single elementary row operation to the identity matrix
related to Row-multiplying transformations · 2
Elementary matrix → So Di, The
related to Row-switching transformations · 2
Elementary matrix → So Ti, The

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Important terminology

matrix row elementary displaystyle det operation identity matrices linear isbn inverse -1 square obtained corresponding elimination operations also mathematics produced

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Elementary matrixis asquare matrix obtained from the application of a single elementary row operation to the identity matrix0.90text
Elementary matrixis adiagonal matrix0.90text
Elementary matrixis aidentity matrix but with an m in the0.90text
Elementary matrixrelated to Elementary row operationsThere0.60section
Elementary matrixrelated to Elementary row operationsIf0.60section
Elementary matrixrelated to Elementary row operationsEA0.60section
Elementary matrixrelated to Elementary row operationsThe0.60section
Elementary matrixrelated to Elementary row operationsThis0.60section
Elementary matrixrelated to Elementary row operationsYoneda0.60section
Elementary matrixrelated to Row-addition transformationsThe0.60section
Elementary matrixrelated to Row-addition transformationsSo Lij0.60section
Elementary matrixrelated to Row-addition transformationsAnd0.60section

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    Min side: 3
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