mathjs/docs/reference/functions/norm.md

Function norm

Calculate the norm of a number, vector or matrix.

The second parameter p is optional. If not provided, it defaults to 2.

Syntax

math.norm(x)
math.norm(x, p)

Parameters

Parameter	Type	Description
x	number | BigNumber | Complex | Array | Matrix	Value for which to calculate the norm
p	number | BigNumber | string	Vector space. Supported numbers include Infinity and -Infinity. Supported strings are: 'inf', '-inf', and 'fro' (The Frobenius norm) Default value: 2.

Returns

Type	Description
number | BigNumber	the p-norm

Examples

math.abs(-3.5);                         // returns 3.5
math.norm(-3.5);                        // returns 3.5

math.norm(math.complex(3, -4));         // returns 5

math.norm([1, 2, -3], Infinity);        // returns 3
math.norm([1, 2, -3], -Infinity);       // returns 1

math.norm([3, 4], 2);                   // returns 5

math.norm([[1, 2], [3, 4]], 1)          // returns 6
math.norm([[1, 2], [3, 4]], 'inf');     // returns 7
math.norm([[1, 2], [3, 4]], 'fro');     // returns 5.477225575051661

See also

abs, hypot