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In mathematics, a '''Redheffer matrix''', studied by {{harvtxt|Redheffer|1977}}, is a [[(0,1) matrix]] whose entries ''a''<sub>''ij''</sub> are 1 if ''i'' divides ''j'' or if ''j'' = 1; otherwise, ''a''<sub>''ij''</sub> = 0.

The [[determinant]] of the ''n''x''n'' [[square matrix|square]] Redheffer matrix is given by the [[Mertens function]] ''M''(''n'').

==Example==
The matrix below is the 12 × 12 Redheffer matrix.
:<math>\left(\begin{smallmatrix}
1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 \\
1 & 1 & 0 & 1 & 0 & 1 & 0 & 1 & 0 & 1 & 0 & 1 \\
1 & 0 & 1 & 0 & 0 & 1 & 0 & 0 & 1 & 0 & 0 & 1 \\
1 & 0 & 0 & 1 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 1 \\
1 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 1 & 0 & 0 \\
1 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 1 \\
1 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 \\
1 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 \\
1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 \\
1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 \\
1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 \\
1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1
\end{smallmatrix}\right)</math>

==References==
*{{Citation | authorlink=Raymond Redheffer | last1=Redheffer | first1=Ray | title=Numerische Methoden bei Optimierungsaufgaben, Band 3 (Tagung, Math. Forschungsinst., Oberwolfach, 1976) | publisher=Birkhäuser | location=Basel, Boston, Berlin | id={{MathSciNet | id = 0468170}} | year=1977 | chapter=Eine explizit lösbare Optimierungsaufgabe | pages=213–216}}

==External links==
*{{MathWorld |title= Redheffer matrix|urlname=RedhefferMatrix}}

[[Category:Matrices]]

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