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)