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Transpose

In linear algebra, transposition is an operation that flips a matrix over its diagonal; that is, transposition switches the row and column indices of the matrix A to produce another matrix, called the transpose of A and often denoted AT (among other notations).

Products, Transpose of a matrix & Transposes of linear maps and bilinear forms

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Transpose of a matrix

ReflectMain diagonalScalarInvolutionAddition
33 related topics

Transposes of linear maps and bilinear forms

Finite-dimensional vector spacesBasesAlgebraic dual spaceModulePullback
20 related topics

Overview

Linear algebraMatrixArthur CayleySymmetric matrixSkew-symmetric matrix
13 related topics

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Overview

Transpose of a matrix

Transposes of linear maps and bilinear forms

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Map overview Semantic statistics

Transpose

Nodes70
Edges69
Triples49
Avg. degree1.97
Density0.028571
Components1

How this topic connects Entity context

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Transpose

Top relations

related to Properties · 16
Transpose → A1A2, A2TA1T, AB, Ak, AkTAk, ATA, By, Eigenvalues, If, In, Jordan, Let, Over, The, This, Together
related to Products · 7
Transpose → AT, But, Furthermore, If, Indeed, Similarly, The
related to Definition · 6
Transpose → AT, Atr, ATWrite, Reflect, TA, The
related to Implementation of matrix transposition on computers · 6
Transpose → BLAS, For, Fourier, However, If, On
is a · 3
Transpose → involution, linear map from the space of m, operation on matrices that may be seen as the representation of some operation on linear maps.This leads to a much more general definition of the transpose that works on every l…
related to Adjoint · 3
Transpose → BX, BY, If
related to Transpose of a bilinear form · 3
Transpose → By, Every, Here
related to Transposes of linear maps and bilinear forms · 3
Transpose → As, In, This
see also · 2
Transpose → Adjugate, Penrose

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Important terminology

matrix displaystyle mathbf linear matrices text map adjoint vector left right spaces space isbn bilinear form product defined algebra similar

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Transposeis ainvolution0.90text
Transposeis alinear map from the space of m0.90text
Transposeis aoperation on matrices that may be seen as the representation of some operation on linear maps.This leads to a much more general definition of the transpose that works on every l…0.90text
Transposerelated to AdjointIf0.60section
Transposerelated to AdjointBX0.60section
Transposerelated to AdjointBY0.60section
Transposerelated to DefinitionThe0.60section
Transposerelated to DefinitionAT0.60section
Transposerelated to DefinitionTA0.60section
Transposerelated to DefinitionAtr0.60section
Transposerelated to DefinitionReflect0.60section
Transposerelated to DefinitionATWrite0.60section

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    Min side: 3
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