SciPy · Class

norm

Computes vector and matrix norms, choosing among norm definitions with ord. It also supports norms over selected axes and batched matrices.

How it works

scipy.linalg.norm selects a vector or matrix norm from the input shape and ord. With axis, it can compute norms across one axis or across batches of matrices; keepdims preserves reduced dimensions, and check_finite controls input validation for finite values.

Syntax

scipy.linalg.norm(a, ord=None, axis=None, keepdims=False, check_finite=True)

Parameters

Name	Type	Description
`a`	`array_like`	Input array whose vector or matrix norm is calculated.
`ord`	`int, inf, -inf, 'fro', 'nuc', None, optional`	Order of the norm; supported choices include integers, `inf`, `-inf`, `'fro'`, `'nuc'`, and `None`.
`axis`	`int, 2-tuple of ints, None, optional`	Axis for vector norms, or a two-axis tuple for matrix norms; `None` selects behavior from input rank.
`keepdims`	`bool, optional`	Whether reduced axes remain as dimensions of length one.
`check_finite`	`bool, optional`	Whether to check that the input contains only finite values.

Returns

nfloat or ndarray: Norm of the matrix or vector(s).

Key points

The function handles both vector and matrix norm calculations.
Matrix inputs support eight norm definitions selected through ord.
Vector inputs can use any supported real-valued order, including infinite orders.
An integer axis produces vector norms along that dimension.
A two-axis tuple lets the function evaluate matrix norms across batched matrices.
The return is a scalar or ndarray containing the requested norm value or values.

Common mistakes

Higher-rank inputs cannot use a specified norm order; use ord=None for tensors beyond matrices and vectors.
Without axis, the input dimensionality determines whether SciPy computes a vector or matrix norm.
Pass NumPy's np.inf or -np.inf for infinite-order norms rather than string representations.

Example: Compute vector and matrix norms

import numpy as np
from scipy.linalg import norm

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

print(norm(x))
print(norm(A, ord="fro"))
print(norm(A, axis=1))

Computes a vector 2-norm, a matrix Frobenius norm, and row-wise vector norms.

When to use it

Vector magnitude

Measure the magnitude of a vector for distance, residual, or convergence calculations.

Matrix analysis

Quantify matrix size using Frobenius, induced, nuclear, or other matrix norms.

Axis-wise and batched reductions

Calculate row, column, or batched-matrix norms without writing reduction loops.

Interview questions

QWhat does scipy.linalg.norm compute, and how does ord affect it?

It computes a matrix or vector norm. The selected definition depends on ord; the function supports eight matrix norms and infinitely many vector norms. For rank other than one or two, only ord=None is supported.

Follow-up: How do you compute norms over batches? Use axis as an integer for vector norms or a two-element tuple for matrix norms.

QHow does axis change the operation?

An integer axis identifies the dimension along which vector norms are computed. A two-tuple identifies the two dimensions containing matrices, so matrix norms are computed over those dimensions.

Follow-up: What happens when axis=None? A one-dimensional input produces a vector norm, while a two-dimensional input produces a matrix norm.

QWhat are the roles of keepdims and check_finite?

keepdims=True retains reduced dimensions with length one, which helps the result broadcast against the original array. The result is a scalar or an array depending on the input and axes.

Follow-up: Why might check_finite=False be used? It can avoid finite-value checking, but inputs containing invalid values may then reach the underlying computation.

scipy.linalg.svdvals
numpy.linalg.norm
scipy.linalg.det

Source: Norm. Checked 2026-10-15.