|
|
|
|
|
|
|
|
|
|
|
Solution
|
Solution provided by AtoZmath.com
|
|
|
|
Diagonally Dominant Matrix checker calculator
|
 1. `[[3,1,2],[2,4,1],[1,1,2]]`
2. `[[-3,0,0],[0,-2,0],[0,0,-1]]`
|
Example1. is Diagonally Dominant Matrix ?
`[[-3,0,0],[0,-2,0],[0,0,-1]]`
Solution:
A Square matrix `A` is called diagonally dominant matrix, if `A_(ii)>=sum_(i!=j)^()|A_(ij)|`
and `A` is called strictly diagonally dominant matrix, if `A_(ii)>sum_(i!=j)^()|A_(ij)|`
`A=[[-3,0,0],[0,-2,0],[0,0,-1]]`
`Row 1:|a_(11)|=|-3|=3,+|a_(12)|+|a_(13)|=+|0|+|0|=0`
`3 >= 0?` yes
`Row 2:|a_(22)|=|-2|=2,+|a_(21)|+|a_(23)|=+|0|+|0|=0`
`2 >= 0?` yes
`Row 3:|a_(33)|=|-1|=1,+|a_(31)|+|a_(32)|=+|0|+|0|=0`
`1 >= 0?` yes
So, given matrix is Diagonally Dominant
|
|
|
|
|
|
