Redheffer matrix (original) (raw)
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.
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| dbo: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) |
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| dbp:title | Redheffer matrix (en) |
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| 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) |
| rdfs:label | Matrice di Redheffer (it) 레드헤퍼 행렬 (ko) Redheffer-matrix (nl) Redheffer matrix (en) Матрица Редхеффера (ru) |
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