Linear algebra in Python

scipy.linalg goes beyond numpy: decompositions, matrix functions, solvers.

import numpy as np
from scipy import linalg

A = np.array([[4.0, 1.0], [1.0, 3.0]])
b = np.array([1.0, 2.0])

print(linalg.solve(A, b).round(4))
print(round(linalg.det(A), 3), round(linalg.norm(A), 4))

values, vectors = linalg.eigh(A)
print(values.round(4), vectors.shape)

lower = linalg.cholesky(A, lower=True)
print(np.allclose(lower @ lower.T, A))
print(linalg.expm(np.zeros((2, 2))).round(1))

How it works

lu, qr and cholesky are the standard decompositions.
eigh is the symmetric case, and faster than eig.
expm is the matrix exponential, not element-wise.

Keywords and builtins used here

as
print
round

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Step 1 of 3 in Linear algebra & signals, step 16 of 23 in Scientific computing with SciPy.

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