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

向量与向量的叉积

a = ( 1 2 3 ) (1) a= \left( \begin{matrix} 1 & 2 & 3 \\ \end{matrix} \right) \tag{1} a=(1​2​3​)(1)

b = ( 4 5 6 ) (2) b= \left( \begin{matrix} 4& 5& 6 \\ \end{matrix} \right) \tag{2} b=(4​5​6​)(2)

c = a ⨂ b = ∣ i j k 1 2 3 4 5 6 ∣ = ( − 3 6 − 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 代码
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]

b 1 = ( 9 2 8 4 5 6 7 8 9 ) (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 ⨂ b 1 = ∣ i j k 1 2 3 9 2 8 ∣ + ∣ i j k 1 2 3 4 5 6 ∣ + ∣ i j k 1 2 3 7 8 9 ∣ = ( 10 19 − 16 − 3 6 − 3 − 6 12 − 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]]

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posted @ 2022-08-19 22:46  luoganttcc  阅读(11)  评论(0)    收藏  举报