矩阵的分数幂

https://scicomp.stackexchange.com/questions/16219/what-is-a-good-way-to-take-fractional-powers-of-a-matrix-in-matlab
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https://docs.scipy.org/doc/scipy/reference/generated/scipy.linalg.fractional_matrix_power.html
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https://math.stackexchange.com/questions/732511/fractional-power-of-matrix
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import numpy as np
from scipy.linalg import fractional_matrix_power
a = np.array([[1.0, 3.0], [1.0, 4.0]])
b = fractional_matrix_power(a, 0.5)

alph = 1/2
V,D=np.linalg.eig(a)

Aalph = D@np.diag((V**alph))@np.linalg.inv(D)
abs(Aalph-b)
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