Lehmer matrix

In <a href="/facts/Mathematics/pxTouaz4">mathematics</a>, particularly <a href="/facts/Matrix_(mathematics)/qa8FI4ko">matrix theory</a>, the n×n Lehmer matrix (named after <a href="/facts/Derrick_Henry_Lehmer/EI61SICa">Derrick Henry Lehmer</a>) is the constant <a href="/facts/Symmetric_matrix/08CGwjNl">symmetric matrix</a> defined by

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

Alternatively, this may be written as

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

Lehmer matrix open-in-new

Lehmer matrix