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@@ -110,7 +110,7 @@ $$\boldsymbol S_b\boldsymbol w=\lambda\boldsymbol S_w\boldsymbol w$$
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$$l(\boldsymbol w)=-\boldsymbol w^T\boldsymbol S_b\boldsymbol w+\lambda(\boldsymbol w^T\boldsymbol S_w\boldsymbol w-1)$$
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对$\boldsymbol w$求偏导可得：
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$$\begin{aligned}
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-\cfrac{\partial l(\boldsymbol w)}{\partial \boldsymbol w} &= -\cfrac{\partial(\boldsymbol w^T\boldsymbol S_b\boldsymbol w)}{\partial \boldsymbol w}+\lambda \cfrac{(\boldsymbol w^T\boldsymbol S_w\boldsymbol w-1)}{\partial \boldsymbol w} \\
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+\cfrac{\partial l(\boldsymbol w)}{\partial \boldsymbol w} &= -\cfrac{\partial(\boldsymbol w^T\boldsymbol S_b\boldsymbol w)}{\partial \boldsymbol w}+\lambda \cfrac{\partial(\boldsymbol w^T\boldsymbol S_w\boldsymbol w-1)}{\partial \boldsymbol w} \\
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&= -(\boldsymbol S_b+\boldsymbol S_b^T)\boldsymbol w+\lambda(\boldsymbol S_w+\boldsymbol S_w^T)\boldsymbol w
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\end{aligned}$$
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又$\boldsymbol S_b=\boldsymbol S_b^T,\boldsymbol S_w=\boldsymbol S_w^T$，则：
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Sm1les