为什么两个不同的旋转矩阵在点积到向量时会给出相同的结果？

Question

我有两个不同的旋转矩阵，当将它们点积为向量时，我得到了相同的结果。这是什么意思？

这里是旋转矩阵和向量

vec = [-7.74299796, 7.28526622, 9.15009209]

rot_mat1 = [[ 0.39713126,  0.85165074, -0.34202014],
            [-0.81079831,  0.15097003, -0.56552114],
            [-0.4299917 ,  0.50189548,  0.7504719 ]]

rot_mat2 = [[ 0.82343558,  0.21636871,  0.52453639],
            [ 0.0429524 ,  0.89801831, -0.43785637],
            [-0.56578171,  0.38307661,  0.73016667]]

结果

[ 0.,  2.203296, 13.852754]

Answer 1

结果不一样：

import numpy as np

vec = np.array([-7.74299796, 7.28526622, 9.15009209])

rot_mat1 = np.array([
    [0.39713126, 0.85165074, -0.34202014],
    [-0.81079831, 0.15097003, -0.56552114],
    [-0.4299917, 0.50189548, 0.7504719]
])
rot_mat2 = np.array([
    [0.82343558, 0.21636871, 0.52453639],
    [0.0429524, 0.89801831, -0.43785637],
    [-0.56578171, 0.38307661, 0.73016667]
])

result1 = np.dot(rot_mat1, vec)
result2 = np.dot(rot_mat2, vec)

print("Result from rot_mat1:", result1)
print("Result from rot_mat2:", result2)

退货者

Result from rot_mat1: [5.36930799e-08 2.20329601e+00 1.38527540e+01]
Result from rot_mat2: [-8.90472861e-08  2.20329601e+00  1.38527540e+01]