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若令$ \boldsymbol{x}=(x_1,x_2,...,x_m)^T $,$ \boldsymbol{x}_{d} $为去均值后的$ \boldsymbol{x} $,$ \boldsymbol{y}=(y_1,y_2,...,y_m)^T $,$ \boldsymbol{y}_{d} $为去均值后的$ \boldsymbol{y} $,其中$ \boldsymbol{x} $、$ \boldsymbol{x}_{d} $、$ \boldsymbol{y} $、$ \boldsymbol{y}_{d} $均为m行1列的列向量,代入上式可得:
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若令$ \boldsymbol{x}=(x_1,x_2,...,x_m)^T $,$ \boldsymbol{x}_{d} $为去均值后的$ \boldsymbol{x} $,$ \boldsymbol{y}=(y_1,y_2,...,y_m)^T $,$ \boldsymbol{y}_{d} $为去均值后的$ \boldsymbol{y} $,其中$ \boldsymbol{x} $、$ \boldsymbol{x}_{d} $、$ \boldsymbol{y} $、$ \boldsymbol{y}_{d} $均为m行1列的列向量,代入上式可得:
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$$ \cfrac{\partial E_{\hat{\boldsymbol w}}}{\partial \hat{\boldsymbol w}}=2\mathbf{X}^T(\mathbf{X}\hat{\boldsymbol w}-\boldsymbol{y}) $$
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$$ \cfrac{\partial E_{\hat{\boldsymbol w}}}{\partial \hat{\boldsymbol w}}=2\mathbf{X}^T(\mathbf{X}\hat{\boldsymbol w}-\boldsymbol{y}) $$
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