向量与向量的叉积和向量与矩阵的叉积数学表达式与python 实现
向量與向量的叉積
a=(123)(1)a= \left( \begin{matrix} 1 & 2 & 3 \\ \end{matrix} \right) \tag{1} a=(1?2?3?)(1)
b=(456)(2)b= \left( \begin{matrix} 4& 5& 6 \\ \end{matrix} \right) \tag{2} b=(4?5?6?)(2)
c=a?b=∣ijk123456∣=(?36?3)(3)c=a\bigotimes b= \begin{vmatrix} i & j & k \\ 1 & 2 & 3 \\ 4& 5& 6 \\ \end{vmatrix}= \left( \begin{matrix} -3 & 6 & -3 \\ \end{matrix} \right) \tag{3} c=a?b=∣∣∣∣∣∣?i14?j25?k36?∣∣∣∣∣∣?=(?3?6??3?)(3)
python 代碼
import numpy as np a=np.array([1,2,3]) b=np.array([4,5,6]) c=np.cross(a,b) print(c) [-3 6 -3]b1=(928456789)(4)b1= \left( \begin{matrix} 9 & 2& 8 \\ 4 & 5 & 6 \\ 7 & 8 & 9 \\ \end{matrix} \right) \tag{4} b1=???947?258?869????(4)
c=a?b1=∣ijk123928∣+∣ijk123456∣+∣ijk123789∣=(1019?16?36?3?612?6)(5)c=a\bigotimes b_1= \begin{vmatrix} i & j & k \\ 1 & 2 & 3 \\ 9& 2& 8 \\ \end{vmatrix}+\begin{vmatrix} i & j & k \\ 1 & 2 & 3 \\ 4& 5& 6 \\ \end{vmatrix}+\begin{vmatrix} i & j & k \\ 1 & 2 & 3 \\ 7& 8& 9 \\ \end{vmatrix}= \left( \begin{matrix} 10 & 19 &-16\\ -3 & 6 & -3\\ -6 & 12& -6 \end{matrix} \right) \tag{5} c=a?b1?=∣∣∣∣∣∣?i19?j22?k38?∣∣∣∣∣∣?+∣∣∣∣∣∣?i14?j25?k36?∣∣∣∣∣∣?+∣∣∣∣∣∣?i17?j28?k39?∣∣∣∣∣∣?=???10?3?6?19612??16?3?6????(5)
b1=np.array([[9,2,8],[4,5,6],[7,8,9]]) print(np.cross(a,b1)) [[ 10 19 -16][ -3 6 -3][ -6 12 -6]]markdown
markdown1
總結
以上是生活随笔為你收集整理的向量与向量的叉积和向量与矩阵的叉积数学表达式与python 实现的全部內容，希望文章能夠幫你解決所遇到的問題。
