1 矩阵(Y=f(x))对标量x求导
矩阵Y是一个(m
imes 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
imes n)的矩阵，函数(y=f(x))对矩阵(X)中的每个元素求偏导，对(m
imes n)矩阵求导后还是(m
imes 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}{partial x_{mn}}end{bmatrix}]
