矩阵求导与转置运算

前言：在推导算法过程中遇到一些数学运算，遇到了就记录下，方便回忆

---

矩阵转置

$$\begin{gathered} (A+B{)}^T=A^T+B^T \\ (AB{)}^T=B^T{A}^T \end{gathered}$$

矩阵求导

$$\begin{gathered} \frac{\partial Ax}{\partial x}=A^T \\ \frac{\partial Ax}{\partial x^T}=A \\ \frac{\partial x^{T}A}{\partial x}=A \end{gathered}$$
$$\frac{\partial x^{T}Ax}{\partial x}=(A^T+A)x$$若A是对称矩阵，即A^T = A，则：
$$\frac{\partial x^{T}Ax}{\partial x}=2Ax$$

---

参考：
向量，标量对向量求导数