更改

TPM矩阵基于可逆性的因果涌现，与其奇异值相关。同样，在规定<math>\epsilon\geq 0</math>之后，我们可以筛选两个协方差矩阵的奇异值来计算因果涌现，即

TPM矩阵基于可逆性的因果涌现，与其奇异值相关。同样，在规定<math>\epsilon\geq 0</math>之后，我们可以筛选两个协方差矩阵的奇异值来计算因果涌现，即

<blockquote>

<blockquote>

<math>\Delta\Gamma_\alpha(\epsilon)\equiv\hat{\gamma}_\alpha(\epsilon)-\hat\gamma_\alpha=\frac{1}{r_\epsilon}(\frac{1}{2}-\frac{\alpha}{4})\sum_{i=1}^{r_\epsilon}\ln s_i+\frac{\alpha}{4r_\epsilon}\sum_{i=1}^{r_\epsilon}\ln\kappa_i-\frac{1}{n}(\frac{1}{2}-\frac{\alpha}{4})\sum_{i=1}^{r}\ln s_i-\frac{\alpha}{4n}\sum_{i=1}^{n}\ln\kappa_i.

<math>\Delta\Gamma_\alpha(\epsilon)\equiv\gamma_\alpha(\epsilon)-\gamma_\alpha=\frac{1}{r_\epsilon}(\frac{1}{2}-\frac{\alpha}{4})\sum_{i=1}^{r_\epsilon}\ln s_i+\frac{\alpha}{4r_\epsilon}\sum_{i=1}^{r_\epsilon}\ln\kappa_i-\frac{1}{n}(\frac{1}{2}-\frac{\alpha}{4})\sum_{i=1}^{r}\ln s_i-\frac{\alpha}{4n}\sum_{i=1}^{n}\ln\kappa_i.

</math>

</math>

</blockquote>

</blockquote>