Lehmer matrix

In mathematics, particularly matrix theory, the n×n Lehmer matrix (named after Derrick Henry Lehmer) is the constant symmetric matrix defined by

${\displaystyle A_{ij}={\begin{cases}i/j,&j\geq i\\j/i,&j<i.\end{cases}}}$

Alternatively, this may be written as

${\displaystyle A_{ij}={\frac {{\mbox{min}}(i,j)}{{\mbox{max}}(i,j)}}.}$