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In mathematics, a Redheffer matrix, often denoted as studied by , is a square (0,1) matrix whose entries aij are 1 if i divides j or if j = 1; otherwise, aij = 0. It is useful in some contexts to express Dirichlet convolution, or convolved divisors sums, in terms of matrix products involving the transpose of the Redheffer matrix.

Attributes	Values
rdf:type	anatomical structure yago:WikicatMatrices yago:Abstraction100002137 yago:Arrangement107938773 yago:Array107939382 yago:Group100031264 yago:Matrix108267640
rdfs:label	Matrice di Redheffer (it) 레드헤퍼 행렬 (ko) Redheffer-matrix (nl) Redheffer matrix (en) Матрица Редхеффера (ru)
rdfs:comment	In mathematics, a Redheffer matrix, often denoted as studied by , is a square (0,1) matrix whose entries aij are 1 if i divides j or if j = 1; otherwise, aij = 0. It is useful in some contexts to express Dirichlet convolution, or convolved divisors sums, in terms of matrix products involving the transpose of the Redheffer matrix. (en) In algebra lineare con matrice di Redheffer si indica una matrice binaria il cui elemento è 1 se j=1 oppure i divide j (incluso il caso in cui i=1). Prende il nome dal matematico americano . Per esempio, la matrice di Redheffer 12x12 è la seguente: La matrice di Redheffer può essere definita per qualunque dimensione mxn, non necessariamente quadrata. Tuttavia, di solito si fa riferimento solo a matrici quadrate, indicando con matrice di Redheffer di ordine n la matrice di dimensione nxn. (it) In de wiskunde, is een Redheffer-matrix, bestudeerd door (1977), een (0,1)-matrix waarvan de elementen aij gelijk aan 1 zijn als i door j deelt of als j=1; anders geldt aij=0. De determinant van de n x n vierkante Redheffer-matrix wordt gegeven door de Mertens-functie M(n) (nl) 수학에서 레드헤퍼 행렬(Redheffer matrix, Redheffer 1977)은 행렬이며, 가 인 경우이거나 가 로 나누어 떨어진다면 가 이다. 그렇지 않으면 이다. 레드헤퍼(Redheffer) 정사각행렬의 행렬식은 메르텐스 함수 에 의해 주어진다. 레드헤퍼행렬은 행렬이자 이진 행렬이다. (ko) В математике матрица Редхеффера, изученная - это (0,1)-матрица, элементы aij которой равны 1, если i делит j или если j = 1, в остальных случаях aij = 0. (ru)
dcterms:subject	Matrices Number theory
Wikipage page ID	22113019 (xsd:integer)
Wikipage revision ID	1114872929 (xsd:integer)
Link from a Wikipage to another Wikipage	Mertens function Euler's phi function Euler phi function Determinant Pentagonal number theorem Riemann Hypothesis Riemann zeta function Characteristic polynomial Generating function transformation Prime omega function Q-Pochhammer symbol Eigenspace Eigenvalue Eigenvector Mobius function Mobius inversion formula Arithmetic function Singular matrix Emission spectrum Matrices Transpose Cyclotomic polynomials Lambert series Square matrix Number theory Euler–Mascheroni constant Partition function (number theory) Dirichlet convolution Dirichlet series Graph theory Jordan normal form Invertible matrix Arithmetic functions Binomial transform Toeplitz matrix Redheffer star product Divisor sum identities Spectral radius Orthogonal polynomials Diagonalizable Moebius inversion Stirling transform Ramanujan sum Dirichlet generating function Dirichlet inverse (0,1) matrix Mobius inversion Moebius function dbr:Anderson-Apostol_divisor_sums
Link from a Wikipage to an external page	https://postimg.cc/bSdYFr5J https://ac.els-cdn.com/S0022314X09001723/1-s2.0-S0022314X09001723-main.pdf%3F_tid=7ae089eb-b00a-4cd3-a6d0-59f6d625178a&acdnat=1544629359_9caf1dc5b5ea630462558327be101556 https://www.researchgate.net/publication/222820191
sameAs	Redheffer matrix Redheffer matrix Redheffer matrix Redheffer matrix Redheffer matrix Redheffer matrix Redheffer matrix Redheffer matrix Redheffer matrix
dbp:wikiPageUsesTemplate	dbt:Citation dbt:Cite_journal dbt:Cite_web dbt:Harvtxt dbt:MathWorld dbt:Reflist dbt:Matrix_classes
title	Redheffer matrix (en)
urlname	RedhefferMatrix (en)
has abstract	In mathematics, a Redheffer matrix, often denoted as studied by , is a square (0,1) matrix whose entries aij are 1 if i divides j or if j = 1; otherwise, aij = 0. It is useful in some contexts to express Dirichlet convolution, or convolved divisors sums, in terms of matrix products involving the transpose of the Redheffer matrix. (en) In algebra lineare con matrice di Redheffer si indica una matrice binaria il cui elemento è 1 se j=1 oppure i divide j (incluso il caso in cui i=1). Prende il nome dal matematico americano . Per esempio, la matrice di Redheffer 12x12 è la seguente: La matrice di Redheffer può essere definita per qualunque dimensione mxn, non necessariamente quadrata. Tuttavia, di solito si fa riferimento solo a matrici quadrate, indicando con matrice di Redheffer di ordine n la matrice di dimensione nxn. (it) In de wiskunde, is een Redheffer-matrix, bestudeerd door (1977), een (0,1)-matrix waarvan de elementen aij gelijk aan 1 zijn als i door j deelt of als j=1; anders geldt aij=0. De determinant van de n x n vierkante Redheffer-matrix wordt gegeven door de Mertens-functie M(n) (nl) 수학에서 레드헤퍼 행렬(Redheffer matrix, Redheffer 1977)은 행렬이며, 가 인 경우이거나 가 로 나누어 떨어진다면 가 이다. 그렇지 않으면 이다. 레드헤퍼(Redheffer) 정사각행렬의 행렬식은 메르텐스 함수 에 의해 주어진다. 레드헤퍼행렬은 행렬이자 이진 행렬이다. (ko) В математике матрица Редхеффера, изученная - это (0,1)-матрица, элементы aij которой равны 1, если i делит j или если j = 1, в остальных случаях aij = 0. (ru)
gold:hypernym	Matrix
prov:wasDerivedFrom	wikipedia-en:Redheffer_matrix?oldid=1114872929&ns=0
page length (characters) of wiki page	27998 (xsd:nonNegativeInteger)
foaf:isPrimaryTopicOf	wikipedia-en:Redheffer_matrix

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