norm

Vector or matrix norm.

Syntax

n = norm(A)
n = norm(A, p)
n = norm(A, 'fro')

Description

Returns the norm of A. The interpretation depends on A’s shape and the p argument:

• For vectors: p = 2 (default) is the Euclidean norm, p = 1 the sum of absolute values, p = Inf the max absolute value, any positive scalar p the p-norm.
• For matrices: p = 2 (default) is the largest singular value, p = 1 the max column sum, p = Inf the max row sum, 'fro' the Frobenius norm (sqrt of sum of squared entries).

Examples

norm([3 4])              % 5    (Euclidean)
norm([3 4], 1)           % 7    (sum of |x|)
norm(magic(3))           % 15   (largest singular value)
norm(magic(3), 'fro')    % ~16.882

See also

• cond — Condition number of a matrix.
• svd — Singular value decomposition.