comparison matrix

In linear algebra, let {{math|1=A = (a_ij)}} be a {{math|n × n}} complex matrix. The comparison matrix {{math|1=M(A) = (α_ij)}} of complex matrix A is defined as

:$\backslash alpha\_\{ij\}\; =\; \backslash begin\{cases\}$

-|a_{ij}| &\text{if } i \neq j, \\

|a_{ij}| &\text{if } i=j. \end{cases}{{cite book |last1=Varga |first1=Richard S. |title=Matrix Iterative Analysis |publisher=Springer Science+Business Media |year=2006 |isbn=1-4020-3555-1 |edition=2nd |page=92 |chapter=Basic Iterative Methods and Comparison Theorems}}