numpy.linalg.norm

numpy.linalg.norm(x, ord=None)

Matrix or vector norm.

Parameters:

x : array_like, shape (M,) or (M, N)

Input array.

ord : {int, 1, -1, 2, -2, inf, -inf, ‘fro’}

Order of the norm (see table under Notes).

Returns:

n : float

Norm of the matrix or vector

Notes

For values ord < 0, the result is, strictly speaking, not a mathematical ‘norm’, but it may still be useful for numerical purposes.

The following norms can be calculated:

ord norm for matrices norm for vectors
None Frobenius norm 2-norm
‘fro’ Frobenius norm
inf max(sum(abs(x), axis=1)) max(abs(x))
-inf min(sum(abs(x), axis=1)) min(abs(x))
1 max(sum(abs(x), axis=0)) as below
-1 min(sum(abs(x), axis=0)) as below
2 2-norm (largest sing. value) as below
-2 smallest singular value as below
other sum(abs(x)**ord)**(1./ord)

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