vault backup: 2023-10-15 16:53:40

Study/DL/吴恩达深度学习课程/矩阵求导.md

@@ -23,8 +23,20 @@ $\frac{dB}{dA} = \frac{d(f(A))}{dA}$ 即 `B` 对 `A` 中的每个变量进行求
 ## 常见公式推导
 1. 
 	$$\begin{aligned}
-	f(X) = A^T \cdot X = \sum_{i=1}^{n}a_i x_i \\
-	d(f(X))
-	
-	
-    $$
+	f(X) &= A^T \cdot X = \sum_{i=1}^{n}a_i x_i \\
+	\frac{d(f(X))}{dX} &= 
+	\left[ \begin{matrix}
+	\frac{\partial{f(X)}}{\partial{x_1}} \\
+	\frac{\partial{f(X)}}{\partial{x_2}} \\
+	\vdots\\
+	\frac{\partial{f(X)}}{\partial{x_n}}
+	\end{matrix} \right]
+	=
+	\left[ \begin{matrix}
+	a_1\\
+	a_2\\
+	\vdots\\
+	a_n
+	\end{matrix} \right]
+	= A
+    \end{aligned}$$