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第471行：
第471行： − + 第478行：
第478行： − Established. On the other hand, there is also an inequality that holds for the entropy of the average vector of all row vectors in P,+ 第484行：
第484行： − + 第490行：
第490行： − +
→Maximum Value
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When <math>P_i</math> is a solitary heat vector without uncertainty, the equal sign of this equation holds. This occurs when <math>P_i</math> is a deterministic one-hot vector. Therefore, when all <math>P_i</math> are one-hot vectors, we have:
When <math>P_i</math> is a one-hot vector without uncertainty, the equal sign of this equation holds. This occurs when <math>P_i</math> is a deterministic one-hot vector. Therefore, when all <math>P_i</math> are one-hot vectors, we have:
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On the other hand, there is also an inequality that holds for the entropy of the average vector of all row vectors in P,
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The equal sign holds when the condition <math>\bar{P}=\frac{1}{N}\cdot \mathbb{1}</math> is satisfied.
The equal sign holds when the condition <math>\bar{P}=\frac{1}{N}\cdot \mathbb{1}</math> is satisfied, where [math]\mathbb{1}[/math] represents the vector with all elements being 1.
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When the equal sign of these two equations holds simultaneously, that is, when <math>P_i</math> is a solitary heat vector and <math>\bar{P}</math> is uniformly distributed (at this time, it is necessary to require [math]P_i[/math] to be perpendicular to each other, that is, P is a [[Permutation Matrix]]) — EI reaches its maximum value of:
When the equal sign of these two equations holds simultaneously, that is, when <math>P_i</math> is a one-hot vector and <math>\bar{P}</math> is uniformly distributed (at this time, it is necessary to require [math]P_i[/math] to be perpendicular to each other, that is, P is a [[Permutation Matrix]]) — EI reaches its maximum value of:
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