矩阵微分系列三:线性变换的导数和最小二乘解
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先回顾一下矩阵乘矩阵的规则:$AB=\sum_{k} a_{ik} b_{kj}$
矩阵乘向量的规则:$A \textbf{x}=\sum_{k} a_{ik} x_{k}$
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公式1:
- $\nabla_X f(AX+B)=A^T \nabla_Y f$, 其中$Y=AX+B$, $A \in R^{m \times n}$, $X \in R^{n \times p}$, $B\in R^{m \times p}$
证明:
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公式2:
证明:
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