21 lines
439 B
Python
21 lines
439 B
Python
|
import numpy as np
|
||
|
|
|
||
|
|
A = np.array([ [1, 5, 1]
|
||
|
|
, [5, 0, -3]
|
||
|
|
, [1, -3, 7]])
|
||
|
|
|
||
|
|
print(np.linalg.eig(A))
|
||
|
|
|
||
|
|
O = np.linalg.eig(A)[1]
|
||
|
|
D = np.zeros((3, 3))
|
||
|
|
for i, v in enumerate(np.linalg.eig(A)[0]):
|
||
|
|
D[i][i] = v
|
||
|
|
|
||
|
|
I = np.zeros((3, 3))
|
||
|
|
for i in range(3):
|
||
|
|
I[i][i] = 1
|
||
|
|
|
||
|
|
print("(2)", np.allclose(np.dot(O.T, O), I))
|
||
|
|
print("(3)", np.allclose(A, np.dot(np.dot(O, D), O.T)))
|
||
|
|
print("(4)", np.allclose(np.dot(A, A), np.dot(np.dot(O, np.dot(D, D)), O.T)))
|