原始矩阵(直接影响矩阵)为


$$Ori=\begin{array}{|c|c|c|c|c|c|c|}\hline {M_{9 \times9}} &A &B &C &D &E &F &G &H &I\\ \hline A &0 &3 &1 &5 &8 &8 &3 &5 &0\\ \hline B &5 &0 &6 &4 &3 &2 &5 &8 &6\\ \hline C &4 &6 &0 &7 &1 &2 &9 &3 &1\\ \hline D &3 &6 &9 &0 &8 &9 &11 &5 &3\\ \hline E &8 &9 &2 &11 &0 &10 &9 &2 &5\\ \hline F &5 &8 &0 &10 &8 &0 &9 &4 &6\\ \hline G &0 &11 &6 &5 &9 &10 &0 &9 &0\\ \hline H &9 &10 &5 &3 &5 &3 &7 &0 &6\\ \hline I &5 &7 &1 &8 &10 &6 &5 &3 &0\\ \hline \end{array} $$

规范直接关系矩阵求解过程 $$ \require{cancel} \require{AMScd} \begin{CD} O @>>>N \\ \end{CD} $$


  • $$\mathcal{N}=\begin{array}{|c|c|c|c|c|c|c|}\hline {M_{9 \times9}} &A &B &C &D &E &F &G &H &I\\ \hline A &0 &0.037 &0.012 &0.061 &0.097 &0.097 &0.037 &0.061 &0\\ \hline B &0.061 &0 &0.073 &0.049 &0.037 &0.024 &0.061 &0.097 &0.073\\ \hline C &0.049 &0.073 &0 &0.085 &0.012 &0.024 &0.11 &0.037 &0.012\\ \hline D &0.037 &0.073 &0.11 &0 &0.097 &0.11 &0.134 &0.061 &0.037\\ \hline E &0.097 &0.11 &0.024 &0.134 &0 &0.122 &0.11 &0.024 &0.061\\ \hline F &0.061 &0.097 &0 &0.122 &0.097 &0 &0.11 &0.049 &0.073\\ \hline G &0 &0.134 &0.073 &0.061 &0.11 &0.122 &0 &0.11 &0\\ \hline H &0.11 &0.122 &0.061 &0.037 &0.061 &0.037 &0.085 &0 &0.073\\ \hline I &0.061 &0.085 &0.012 &0.097 &0.122 &0.073 &0.061 &0.037 &0\\ \hline \end{array} $$

综合影响矩阵求解过程 $$\begin{CD} N @>>>T \\ \end{CD} $$



  综合影响矩阵如下

$T=\mathcal{N}(I-\mathcal{N})^{-1}$

$$T=\begin{array}{|c|c|c|c|c|c|c|}\hline {M_{9 \times9}} &A &B &C &D &E &F &G &H &I\\ \hline A &0.056 &0.119 &0.056 &0.132 &0.162 &0.163 &0.118 &0.112 &0.044\\ \hline B &0.117 &0.091 &0.119 &0.123 &0.113 &0.099 &0.143 &0.153 &0.111\\ \hline C &0.092 &0.148 &0.049 &0.143 &0.081 &0.092 &0.176 &0.095 &0.047\\ \hline D &0.115 &0.199 &0.171 &0.113 &0.197 &0.209 &0.247 &0.146 &0.095\\ \hline E &0.171 &0.231 &0.098 &0.238 &0.119 &0.228 &0.228 &0.119 &0.12\\ \hline F &0.133 &0.212 &0.071 &0.216 &0.198 &0.108 &0.217 &0.132 &0.127\\ \hline G &0.083 &0.244 &0.135 &0.161 &0.196 &0.207 &0.118 &0.184 &0.066\\ \hline H &0.172 &0.219 &0.116 &0.129 &0.151 &0.127 &0.179 &0.078 &0.119\\ \hline I &0.129 &0.188 &0.073 &0.188 &0.208 &0.166 &0.164 &0.11 &0.054\\ \hline \end{array} $$