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In mathematics, a generalized permutation matrix (or monomial matrix) is a matrix with the same nonzero pattern as a permutation matrix, i.e. there is exactly one nonzero entry in each row and each column. Unlike a permutation matrix, where the nonzero entry must be 1, in a generalized permutation matrix the nonzero entry can be any nonzero value. An example of a generalized permutation matrix is

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rdfs:label	Monomiale Matrix (de) Generalized permutation matrix (en) 一般化置換行列 (ja)
rdfs:comment	Eine monomiale Matrix oder verallgemeinerte Permutationsmatrix ist in der Mathematik eine quadratische Matrix, bei der in jeder Zeile und jeder Spalte genau ein Eintrag ungleich null ist. Monomiale Matrizen stellen damit eine Verallgemeinerung gewöhnlicher Permutationsmatrizen dar, bei denen genau ein Eintrag pro Zeile und Spalte gleich eins ist. Die regulären monomialen Matrizen bilden mit der Matrizenmultiplikation als Verknüpfung die . Monomiale Matrizen werden unter anderem in der Geometrie, der Gruppentheorie und der Kodierungstheorie verwendet. (de) In mathematics, a generalized permutation matrix (or monomial matrix) is a matrix with the same nonzero pattern as a permutation matrix, i.e. there is exactly one nonzero entry in each row and each column. Unlike a permutation matrix, where the nonzero entry must be 1, in a generalized permutation matrix the nonzero entry can be any nonzero value. An example of a generalized permutation matrix is (en) 数学の分野において、一般化置換行列（いっぱんかちかんぎょうれつ、英: generalized permutation matrix）あるいは単項行列（たんこうぎょうれつ、英: monomial matrix）とは、置換行列と同様の非ゼロ成分の配置パターン、すなわち、各列と各行に必ず唯一つの非ゼロ成分が存在するようなパターンを持つ行列であるが、それらの成分が必ず 1 である置換行列とは異なり、一般化置換行列ではそれらの成分は非ゼロであればどのような値でもよい。次の行列は、一般化置換行列の一例である： (ja)
dcterms:subject	Sparse matrices Permutations Matrices
Wikipage page ID	246320 (xsd:integer)
Wikipage revision ID	1094897505 (xsd:integer)
Link from a Wikipage to another Wikipage	Representation theory Sparse matrices Hyperoctahedral group Permutation Permutation matrix Unit (ring theory) Index of a subgroup Permutation matrices Signed permutation matrices Permutations Cross-polytope Mathematics Matrix (mathematics) General linear group Generalized symmetric group Normal subgroup Quotient group Monomial representation Roots of unity Demihypercube Subgroup Matrices Semigroup Field (mathematics) Diagonal matrix Ring (mathematics) Wreath product Invertible matrix Coxeter group Hypercube Abelian group Abuse of notation Maximal torus Group isomorphism If and only if Integer Order (group theory) Orthogonal group Semidirect product Set (mathematics) Nonnegative matrices Image (mathematics) Symmetric group Weyl group Linear representation Normalizer Centralizer Sign of a permutation
sameAs	Generalized permutation matrix Generalized permutation matrix Generalized permutation matrix Generalized permutation matrix Generalized permutation matrix Generalized permutation matrix Generalized permutation matrix Generalized permutation matrix
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has abstract	Eine monomiale Matrix oder verallgemeinerte Permutationsmatrix ist in der Mathematik eine quadratische Matrix, bei der in jeder Zeile und jeder Spalte genau ein Eintrag ungleich null ist. Monomiale Matrizen stellen damit eine Verallgemeinerung gewöhnlicher Permutationsmatrizen dar, bei denen genau ein Eintrag pro Zeile und Spalte gleich eins ist. Die regulären monomialen Matrizen bilden mit der Matrizenmultiplikation als Verknüpfung die . Monomiale Matrizen werden unter anderem in der Geometrie, der Gruppentheorie und der Kodierungstheorie verwendet. (de) In mathematics, a generalized permutation matrix (or monomial matrix) is a matrix with the same nonzero pattern as a permutation matrix, i.e. there is exactly one nonzero entry in each row and each column. Unlike a permutation matrix, where the nonzero entry must be 1, in a generalized permutation matrix the nonzero entry can be any nonzero value. An example of a generalized permutation matrix is (en) 数学の分野において、一般化置換行列（いっぱんかちかんぎょうれつ、英: generalized permutation matrix）あるいは単項行列（たんこうぎょうれつ、英: monomial matrix）とは、置換行列と同様の非ゼロ成分の配置パターン、すなわち、各列と各行に必ず唯一つの非ゼロ成分が存在するようなパターンを持つ行列であるが、それらの成分が必ず 1 である置換行列とは異なり、一般化置換行列ではそれらの成分は非ゼロであればどのような値でもよい。次の行列は、一般化置換行列の一例である： (ja)
prov:wasDerivedFrom	wikipedia-en:Generalized_permutation_matrix?oldid=1094897505&ns=0
page length (characters) of wiki page	6240 (xsd:nonNegativeInteger)
foaf:isPrimaryTopicOf	wikipedia-en:Generalized_permutation_matrix
is Link from a Wikipage to another Wikipage of	Monomial Permutation matrix List of named matrices List of permutation topics Signed permutation Signed permutation matrices Signed permutation matrix

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