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Permutation matrix

In mathematics, particularly in matrix theory, a permutation matrix is a square binary matrix that has exactly one entry of 1 in each row and each column with all other entries 0.: 26 An n × n permutation matrix can represent a permutation of n elements. Pre-multiplying an n-row matrix M by a permutation matrix P, forming PM, results in permuting the…

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Overview

Multiplying permutation matrices

Matrix group

Doubly stochastic matrices

Linear-algebraic properties

Restricted forms

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Permutation matrix

Nodes51
Edges50
Triples17
Avg. degree1.96
Density0.039216
Components1

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Permutation matrix

Top relations

related to The transpose is also the inverse · 6
Permutation matrix → Artin, If, PP, The, When, Whenever
related to Doubly stochastic matrices · 5
Permutation matrix → Birkhoff, Every, Neumann, The, The Birkhoff
related to Linear-algebraic properties · 3
Permutation matrix → Just, So, We
is a · 1
Permutation matrix → square binary matrix that has exactly one entry of 1 in each row and each column with all other entries 0
related to Restricted forms · 1
Permutation matrix → Costas
see also · 1
Permutation matrix → Alternating

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Important terminology

displaystyle permutation matrix pi matrices -1 entries group two entry product rows columns permutations row mathsf transpose first th text

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Permutation matrixis asquare binary matrix that has exactly one entry of 1 in each row and each column with all other entries 00.90text
Permutation matrixrelated to Doubly stochastic matricesEvery0.60section
Permutation matrixrelated to Doubly stochastic matricesThe0.60section
Permutation matrixrelated to Doubly stochastic matricesBirkhoff0.60section
Permutation matrixrelated to Doubly stochastic matricesThe Birkhoff0.60section
Permutation matrixrelated to Doubly stochastic matricesNeumann0.60section
Permutation matrixrelated to Linear-algebraic propertiesJust0.60section
Permutation matrixrelated to Linear-algebraic propertiesSo0.60section
Permutation matrixrelated to Linear-algebraic propertiesWe0.60section
Permutation matrixrelated to Restricted formsCostas0.60section
Permutation matrixrelated to The transpose is also the inverseArtin0.60section
Permutation matrixrelated to The transpose is also the inverseIf0.60section

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