矩阵的转置与求导运算 |
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1.矩阵转置 ( A + B ) T = A T + B T (A+B)^{T}=A^{T}+B^{T} (A+B)T=AT+BT ( A B ) T = B T A T (A B)^{T}=B^{T} A^{T} (AB)T=BTAT 2.矩阵求导 ∂ A x ∂ x = A T \frac{\partial A x}{\partial x}=A^{T} ∂x∂Ax=AT ∂ A x ∂ x T = A \frac{\partial A x}{\partial x^{T}}=A ∂xT∂Ax=A ∂ x T A ∂ x = A \frac{\partial x^{T} A}{\partial x}=A ∂x∂xTA=A ∂ x T A x ∂ x = ( A T + A ) x \frac{\partial x^{T} A x}{\partial x}=\left(A^{T}+A\right) x ∂x∂xTAx=(AT+A)x python代码：矩阵的转置 import numpy as np arr1 = [[1, 2, 3], [4, 5, 6]] arr2 = np.transpose((arr1)) print(arr2)结果为： [[1 4] [2 5] [3 6]] |
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