Menu
Home
People
Places
Arts
History
Plants & Animals
Science
Life & Culture
Technology
Reference.org
Redheffer matrix
open-in-new
<p>In mathematics, a Redheffer matrix, often denoted A n {\displaystyle A_{n}} as studied by Redheffer (1977), is a <a href="/facts/Square_matrix/5TP9mNNn">square</a> <a href="/facts/(0,1)_matrix/pS4BnBzj">(0,1) matrix</a> whose entries <i>a</i><i>ij</i> are 1 if <i>i</i> divides <i>j</i> or if <i>j</i> = 1; otherwise, <i>a</i><i>ij</i> = 0. It is useful in some contexts to express <a href="/facts/Dirichlet_convolution/DjuhDu1L">Dirichlet convolution</a>, or convolved <a href="/facts/Divisor_sum_identities/XYStEv0K">divisors sums</a>, in terms of matrix products involving the <a href="/facts/Transpose/8wmsagGS">transpose</a> of the n t h {\displaystyle n^{th}} Redheffer matrix. </p>