# 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

``````norm(x)
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

``````abs(-3.5);                         // returns 3.5
norm(-3.5);                        // returns 3.5

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

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

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

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