常用性质

转置

• $(A+B)^T = A^T + B^T$
• $(AB)^T=B^TA^T$

取逆

• $(AB)^{-1} = B^{-1}A^{-1}$

可交换的运算

• $(A^T)^{-1} = (A^{-1})^T$
• $|A^{-1}| = |A|^{-1}$

矩阵求导

• $\frac{\partial x^{T} a}{\partial x}=\frac{\partial a^{T} x}{\partial x}=a$
• $\frac{\partial x^{T} A x}{\partial x}=A x+A^{T} x$