Python程序與矩陣和矢量叉積

Question

我寫了， 給定的矩陣3的a矢量a1，a2，a3 python程序進行操作，它計算一個矩陣3個矢量b1，b2，b3在的b下列方式：

三重產品（分母）就是決定因素。

爲了檢查程序工作，這種關係必須滿足：

換句話說：

det(b) = 1/det(a)

在節目我都小心使用cross和np array。然而，它並沒有滿足上述關係：

import numpy as np 
from numpy import pi as pi 

# 'a' matrix: 
a = np.array([[ 0.291761097764E+01 , 0.000000000000E+00 , 0.574463427333E+01 ], 
       [ -0.145880548882E+01 , 0.252672522500E+01 , 0.574463427333E+01 ], 
       [ -0.145880548882E+01 ,-0.252672522500E+01 , 0.574463427333E+01 ]]) 

# 'a' vectors: 
a_1 = [ 0.291761097764E+01 , 0.000000000000E+00 , 0.574463427333E+01 ] 
a_2 = [ -0.145880548882E+01 , 0.252672522500E+01 , 0.574463427333E+01 ] 
a_3 = [ -0.145880548882E+01 ,-0.252672522500E+01 , 0.574463427333E+01 ] 

# volume of 'a' matrix: 
V_a = np.linalg.det(a) 
print 'V_a = ', V_a 

cte = (2*pi)/V_a 

VEC_1 = np.cross(a_2, a_3) 
VEC_2 = np.cross(a_3, a_1) 
VEC_3 = np.cross(a_1, a_2) 

# calculation of 'b' vectors: 
b_1 = cte * VEC_1 
b_2 = cte * VEC_2 
b_3 = cte * VEC_3 

print 'b_1 = ', b_1 
print 'b_2 = ', b_2 
print 'b_3 = ', b_3 

# building 'b' matrix: 
b = np.vstack ([ b_1 , b_2, b_3 ]) 
print 'b = ', b 

# volume of 'b' matrix: 
V_b = np.linalg.det(b) 
print 'V_b = ', V_b 
print "1/V_a = ", 1/V_a 

print "1/V_a should be equal to V_b; however, we do not get this equality" 

EDIT：顯示的最後一個方程是不正確的。以下應更確切：

Answer 1

你應該有什麼是1/V_a=V_b/(8*pi**3)，而不是1/V_a=V_b（如你在PRINTSCREEN你的最後一個方程忽略了2*pi），當你運行代碼前確實持有。