特征结构的计算与说明


原始矩阵(直接影响矩阵)为


$$Ori=\begin{array}{|c|c|c|c|c|c|c|}\hline {M_{13 \times13}} &A1 &A2 &B1 &B2 &C1 &C2 &C3 &C4 &D1 &D2 &D3 &E1 &E2\\ \hline A1 &0 &31 &12 &46 &43 &34 &38 &24 &45 &23 &40 &30 &18\\ \hline A2 &25 &0 &19 &18 &38 &27 &27 &17 &36 &22 &44 &20 &9\\ \hline B1 &18 &38 &0 &39 &51 &34 &32 &19 &36 &42 &29 &34 &16\\ \hline B2 &24 &14 &16 &0 &45 &45 &24 &30 &36 &28 &33 &36 &22\\ \hline C1 &25 &26 &18 &21 &0 &36 &16 &21 &33 &25 &31 &36 &28\\ \hline C2 &19 &23 &45 &30 &32 &0 &14 &18 &23 &29 &25 &36 &34\\ \hline C3 &21 &24 &25 &37 &29 &27 &0 &28 &36 &32 &32 &27 &30\\ \hline C4 &32 &30 &21 &38 &31 &31 &36 &0 &31 &28 &27 &26 &26\\ \hline D1 &18 &29 &50 &21 &35 &50 &26 &33 &0 &31 &30 &42 &31\\ \hline D2 &14 &24 &27 &24 &23 &27 &36 &19 &35 &0 &17 &18 &35\\ \hline D3 &20 &19 &26 &15 &20 &23 &27 &15 &22 &29 &0 &28 &27\\ \hline E1 &30 &30 &34 &34 &43 &34 &29 &34 &28 &32 &43 &0 &41\\ \hline E2 &10 &15 &21 &12 &22 &10 &18 &20 &12 &28 &18 &16 &0\\ \hline \end{array} $$

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


  • $$\mathcal{N}=\begin{array}{|c|c|c|c|c|c|c|}\hline {M_{13 \times13}} &A1 &A2 &B1 &B2 &C1 &C2 &C3 &C4 &D1 &D2 &D3 &E1 &E2\\ \hline A1 &0 &0.057 &0.022 &0.085 &0.079 &0.062 &0.07 &0.044 &0.083 &0.042 &0.074 &0.055 &0.033\\ \hline A2 &0.046 &0 &0.035 &0.033 &0.07 &0.05 &0.05 &0.031 &0.066 &0.04 &0.081 &0.037 &0.017\\ \hline B1 &0.033 &0.07 &0 &0.072 &0.094 &0.062 &0.059 &0.035 &0.066 &0.077 &0.053 &0.062 &0.029\\ \hline B2 &0.044 &0.026 &0.029 &0 &0.083 &0.083 &0.044 &0.055 &0.066 &0.051 &0.061 &0.066 &0.04\\ \hline C1 &0.046 &0.048 &0.033 &0.039 &0 &0.066 &0.029 &0.039 &0.061 &0.046 &0.057 &0.066 &0.051\\ \hline C2 &0.035 &0.042 &0.083 &0.055 &0.059 &0 &0.026 &0.033 &0.042 &0.053 &0.046 &0.066 &0.062\\ \hline C3 &0.039 &0.044 &0.046 &0.068 &0.053 &0.05 &0 &0.051 &0.066 &0.059 &0.059 &0.05 &0.055\\ \hline C4 &0.059 &0.055 &0.039 &0.07 &0.057 &0.057 &0.066 &0 &0.057 &0.051 &0.05 &0.048 &0.048\\ \hline D1 &0.033 &0.053 &0.092 &0.039 &0.064 &0.092 &0.048 &0.061 &0 &0.057 &0.055 &0.077 &0.057\\ \hline D2 &0.026 &0.044 &0.05 &0.044 &0.042 &0.05 &0.066 &0.035 &0.064 &0 &0.031 &0.033 &0.064\\ \hline D3 &0.037 &0.035 &0.048 &0.028 &0.037 &0.042 &0.05 &0.028 &0.04 &0.053 &0 &0.051 &0.05\\ \hline E1 &0.055 &0.055 &0.062 &0.062 &0.079 &0.062 &0.053 &0.062 &0.051 &0.059 &0.079 &0 &0.075\\ \hline E2 &0.018 &0.028 &0.039 &0.022 &0.04 &0.018 &0.033 &0.037 &0.022 &0.051 &0.033 &0.029 &0\\ \hline \end{array} $$

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



  综合影响矩阵如下

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

$$T=\begin{array}{|c|c|c|c|c|c|c|}\hline {M_{13 \times13}} &A1 &A2 &B1 &B2 &C1 &C2 &C3 &C4 &D1 &D2 &D3 &E1 &E2\\ \hline A1 &0.069 &0.134 &0.108 &0.166 &0.181 &0.161 &0.15 &0.118 &0.175 &0.133 &0.167 &0.147 &0.119\\ \hline A2 &0.099 &0.064 &0.103 &0.101 &0.151 &0.128 &0.114 &0.089 &0.14 &0.113 &0.153 &0.111 &0.086\\ \hline B1 &0.102 &0.147 &0.087 &0.155 &0.196 &0.162 &0.141 &0.109 &0.162 &0.166 &0.149 &0.154 &0.116\\ \hline B2 &0.106 &0.1 &0.109 &0.081 &0.176 &0.171 &0.119 &0.122 &0.152 &0.135 &0.147 &0.15 &0.12\\ \hline C1 &0.101 &0.112 &0.104 &0.109 &0.089 &0.145 &0.098 &0.099 &0.137 &0.121 &0.134 &0.14 &0.121\\ \hline C2 &0.092 &0.11 &0.151 &0.127 &0.149 &0.086 &0.098 &0.096 &0.124 &0.131 &0.127 &0.142 &0.132\\ \hline C3 &0.099 &0.115 &0.122 &0.143 &0.148 &0.139 &0.077 &0.117 &0.15 &0.14 &0.143 &0.132 &0.13\\ \hline C4 &0.12 &0.127 &0.116 &0.148 &0.154 &0.148 &0.141 &0.07 &0.146 &0.135 &0.138 &0.133 &0.125\\ \hline D1 &0.103 &0.135 &0.175 &0.128 &0.172 &0.188 &0.132 &0.134 &0.1 &0.151 &0.152 &0.169 &0.143\\ \hline D2 &0.078 &0.105 &0.115 &0.11 &0.124 &0.125 &0.128 &0.092 &0.136 &0.073 &0.106 &0.105 &0.128\\ \hline D3 &0.084 &0.091 &0.107 &0.09 &0.112 &0.111 &0.108 &0.08 &0.108 &0.117 &0.069 &0.115 &0.109\\ \hline E1 &0.125 &0.137 &0.148 &0.151 &0.187 &0.164 &0.14 &0.137 &0.152 &0.153 &0.176 &0.098 &0.161\\ \hline E2 &0.055 &0.07 &0.082 &0.068 &0.096 &0.071 &0.078 &0.075 &0.074 &0.099 &0.083 &0.078 &0.046\\ \hline \end{array} $$