Generalized permutation matrix

<p>In <a href="/facts/Mathematics/pxTouaz4">mathematics</a>, a generalized permutation matrix (or monomial matrix) is a <a href="/facts/Matrix_(mathematics)/qa8FI4ko">matrix</a> with the same nonzero pattern as a <a href="/facts/Permutation_matrix/xC1ran5s">permutation matrix</a>, i.e. there is exactly one nonzero entry in each row and each column. Unlike a permutation matrix, where the nonzero entry must be 1, in a generalized permutation matrix the nonzero entry can be any nonzero value. An example of a generalized permutation matrix is
</p>

[
            
              
                
                  0
                
                
                  0
                
                
                  3
                
                
                  0
                
              
              
                
                  0
                
                
                  −
                  7
                
                
                  0
                
                
                  0
                
              
              
                
                  1
                
                
                  0
                
                
                  0
                
                
                  0
                
              
              
                
                  0
                
                
                  0
                
                
                  0
                
                
                  
                    
                      2
                    
                  
                
              
            
            ]
          
        
        .
      
    
    {\displaystyle {\begin{bmatrix}0&0&3&0\\0&-7&0&0\\1&0&0&0\\0&0&0&{\sqrt {2}}\end{bmatrix}}.}

Generalized permutation matrix open-in-new

Generalized permutation matrix