向量积的求导法则

时间:2024-03-02 22:33:08

 向量积对列向量X求导运算法则:

注意与标量求导有点不同。

d(UV\')/dX = (dU/dX)V\' + U(dV\'/dX)

d(U\'V)/dX = (dU\'/dX)V + (dV\'/dX)U

重要结论:

d(X\'A)/dX = (dX\'/dX)A + (dA/dX)X\' = IA + 0X\' = A

d(AX)/dX\' = (d(X\'A\')/dX)\' = (A\')\' = A

d(X\'AX)/dX = (dX\'/dX)AX + (d(AX)\'/dX)X = AX + A\'X