对角占优矩阵（Diagonally-dominant Matrix）
作用：它较多出现于经济价值模型和反网络系统的系数矩阵及解某些确定微分方程的数值解法中（来自百度百科）
For some matrices you can see quickly that they are invertible because every number a i i a_{ii} aii on their main diagonal dominates the off-diagonal part of that row i i i
对角占优矩阵是 可逆的
例1：
∣ a 11 ∣ = 3 > ∣ a 12 ∣ + ∣ a 13 ∣ = 1 + 1 = 2 ∣ a 22 ∣ = 3 > ∣ a 21 ∣ + ∣ a 23 ∣ = 1 + 1 = 2 ∣ a 33 ∣ = 3 > ∣ a 31 ∣ + ∣ a 32 ∣ = 1 + 1 = 2 |a_{11}|=3\gt |a_{12}|+|a_{13}|=1+1=2\\ |a_{22}|=3\gt |a_{21}|+|a_{23}|=1+1=2\\ |a_{33}|=3\gt |a_{31}|+|a_{32}|=1+1=2 ∣a11∣=3>∣a12∣+∣a13∣=1+1=2∣a22∣=3>∣a21∣+∣a23∣=1+1=2∣a33∣=3>∣a31∣+∣a32∣=1+1=2
So A A A is diagonally-dominant （ 3 > 2 3\gt 2 3>2）
例2：
2 = ∣ a 11 ∣ = ∣ a 12 ∣ + ∣ a 13 ∣ = 1 + 1 = 2 2 = ∣ a 22 ∣ = ∣ a 21 ∣ + ∣ a 23 ∣ = 1 + 1 = 2 3 = ∣ a 33 ∣ > ∣ a 31 ∣ + ∣ a 32 ∣ = 1 + 1 = 2 2=|a_{11}|= |a_{12}|+|a_{13}|=1+1=2\\ 2=|a_{22}|= |a_{21}|+|a_{23}|=1+1=2\\ 3=|a_{33}|\gt |a_{31}|+|a_{32}|=1+1=2 2=∣a11∣=∣a12∣+∣a13∣=1+1=22=∣a22∣=∣a21∣+∣a23∣=1+1=23=∣a33∣>∣a31∣+∣a32∣=1+1=2
So B B B is NOT diagonally-dominant，but still Invertible（ d e t ( B ) ≠ 0 det(B)\neq 0 det(B)=0）文章来源：https://www.toymoban.com/news/detail-472582.html
例3：
These column vectors are independent，So C is singular and NOT Invertible文章来源地址https://www.toymoban.com/news/detail-472582.html
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