机器学习：深入理解矩阵和向量的求导——第二部分：矩阵与单变量求导

2.1 矩阵对单变量求导

矩阵对单变量的求导与向量求导类似，就是每个元素分别对变量求导。

设$Y=\left[\begin{array}{ccc}{y}_{11}& ...& y_{1n}\\ ...& ...& ...\\ y_{m1}& ...& y_{mn}\end{array}\right]$，则$\frac{\partial Y}{\partial x}=\left[\begin{array}{ccc}\frac{\partial y_{11}}{\partial x}& ...& \frac{\partial y_{1n}}{\partial x}\\ ...& ...& ...\\ \frac{\partial y_{m1}}{\partial x}& ...& \frac{\partial y_{mn}}{\partial x}\end{array}\right]$

2.2 单变量对矩阵求导

设 X = [ x 11 . . . x 1 n . . . . . . . . . x m 1 . . . x m n ] X= \begin{bmatrix} x_{11} & ... & x_{1n} \\ ... & ... & ... \\ x_{m1} & ... & x_{mn} \end{bmatrix}