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import numpy as np
from numpy.linalg import svd
# define your matrix as a 2D numpy array
A = np.array([[4, 0], [3, -5]])
U, S, VT = svd(A)
print("Left Singular Vectors:")
print(U)
print("Singular Values:")
print(np.diag(S))
print("Right Singular Vectors:")
print(VT)
# check that this is an exact decomposition
# @ is used for matrix multiplication in Py3, use np.matmul with Py2
print(U @ np.diag(S) @ VT)
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