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