1. Definition & Examples
1. is Strictly 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 Strictly Diagonally Dominant
2. is Strictly Diagonally Dominant Matrix ?
`[[3,1,2],[2,4,1],[1,1,2]]`
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=[[3,1,2],[2,4,1],[1,1,2]]`
`Row 1:|a_(11)|=|3|=3,+|a_(12)|+|a_(13)|=+|1|+|2|=3`
`3 > 3?` no
`Row 2:|a_(22)|=|4|=4,+|a_(21)|+|a_(23)|=+|2|+|1|=3`
`4 > 3?` yes
`Row 3:|a_(33)|=|2|=2,+|a_(31)|+|a_(32)|=+|1|+|1|=2`
`2 > 2?` no
So, given matrix is not Strictly Diagonally Dominant
This material is intended as a summary. Use your textbook for detail explanation.
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