alpha

1 矩阵\(Y=f(x)\)对标量x求导 矩阵Y是一个\(m\times n\)的矩阵，对标量x求导，相当于矩阵中每个元素对x求导 \[\frac{dY}{dx}=\begin{bmatrix}\dfrac{df_{11}(x)}{dx} & \ldots & \dfrac{df_{1n}(x)}{dx} \\ \vdots & \ddots &\vdots \\ \dfrac{df_{m1}(x)}{dx} & \ldots & \dfrac{df_{mn}(x)}{dx} \end{bmatrix}\] 2 标量y=f(x)对矩阵X求导 注意与上面不同，这次括号内是求偏导，\(X\)是是一个\(m\times n\)的矩阵，函数\(y=f(x)\)对矩阵\(X\)中的每个元素求偏导，对\(m\times n\)矩阵求导后还是\(m\times n\)矩阵 \[\frac{dy}{dX} = \begin{bmatrix}\dfrac{\partial f}{\partial x_{11}} & \ldots & \dfrac{\partial f}{\partial x_{1n}}\\ \vdots & \ddots & \vdots \\\dfrac{\partial f}{\partial x_{m1}} & \ldots & \dfrac{\partial f}{