Comparison matrix

In linear algebra, let A = (a_ij) be a n × n complex matrix. The comparison matrix M(A) = (α_ij) of complex matrix A is defined as

${\displaystyle \alpha _{ij}={\begin{cases}-|a_{ij}|&{\text{if }}i\neq j,\\|a_{ij}|&{\text{if }}i=j.\end{cases}}}$^[1]