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


 * $$\alpha_{ij} = \begin{cases}

-|a_{ij}| &\text{if } i \neq j,  \\
 * a_{ij}| &\text{if } i=j.  \end{cases}$$