# norm

Quaternion norm

## Syntax

``N = norm(quat)``

## Description

example

````N = norm(quat)` returns the norm of the quaternion, `quat`.Given a quaternion of the form $Q=a+b\text{i}+c\text{j}+d\text{k}$, the norm of the quaternion is defined as $\text{norm}\left(Q\right)=\sqrt{{a}^{2}+{b}^{2}+{c}^{2}+{d}^{2}}$.```

## Examples

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Create a scalar quaternion and calculate its norm.

```quat = quaternion(1,2,3,4); norm(quat)```
```ans = 5.4772 ```

The quaternion norm is defined as the square root of the sum of the quaternion parts squared. Calculate the quaternion norm explicitly to verify the result of the `norm` function.

```[a,b,c,d] = parts(quat); sqrt(a^2+b^2+c^2+d^2)```
```ans = 5.4772 ```

## Input Arguments

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Quaternion for which to calculate the norm, specified as a scalar, vector, matrix, or multidimensional array of quaternions.

Data Types: `quaternion`

## Output Arguments

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Quaternion norm. If the input `quat` is an array, the output is returned as an array the same size as `quat`. Elements of the array are real numbers with the same data type as the underlying data type of the quaternion, `quat`.

Data Types: `single` | `double`

## Extended Capabilities

### Objects

Introduced in R2021a 