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这里，[math]|P|_{\alpha}[/math]为矩阵P的[[Schatten范数]]，[math]\Gamma_{\alpha}[/math]为[[近似动力学可逆性]]指标，[math]\sigma_i[/math]为概率转移矩阵P的奇异值，并且按照从大到小的顺序排列，[math]\alpha\in(0,2)[/math]为一个指定的参数，它起到让[math]\Gamma_{\alpha}[/math]能够更多地反映'''确定性'''还是'''简并性'''这样一种权重或倾向性。事实上，不难看出，如果让[math]\alpha\rightarrow 0[/math]，则[math]\Gamma_{\alpha}[/math]就退化成了矩阵P的秩，即：

Here, [math]|P|_{\alpha}[/math] is the [[Schatten norm]] of matrix P, [math]\Gamma_{\alpha}[/math] is the [[Approximate Dynamic Reversibility]] index, [math]\sigma_i[/math] is the singular value of the probability transition matrix P, and is arranged in descending order. [math]\alpha\in(0,2)[/math] is a specified parameter that allows [math]\Gamma_{\alpha}[/math] to reflect more of the weight or tendency of '''Determinism''' or '''Degeneracy'''. In fact, it is not difficult to see that if we let [math]\alpha\rightarrow 0[/math], then [math]\Gamma_{\alpha}[/math] degenerates into the rank of matrix P, that is:

 

 

 

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