# normalize

Quaternion normalization

Since R2020a

## Syntax

``quatNormalized = normalize(quat)``

## Description

example

````quatNormalized = normalize(quat)` normalizes the quaternion.Given a quaternion of the form $Q=a+b\text{i}+c\text{j}+d\text{k}$, the normalized quaternion is defined as $Q/\sqrt{{a}^{2}+{b}^{2}+{c}^{2}+{d}^{2}}$.```

## Examples

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Quaternions can represent rotations when normalized. You can use `normalize` to normalize a scalar, elements of a matrix, or elements of a multi-dimensional array of quaternions. Create a column vector of quaternions, then normalize them.

```quatArray = quaternion([1,2,3,4; ... 2,3,4,1; ... 3,4,1,2]); quatArrayNormalized = normalize(quatArray)```
```quatArrayNormalized = 3x1 quaternion array 0.18257 + 0.36515i + 0.54772j + 0.7303k 0.36515 + 0.54772i + 0.7303j + 0.18257k 0.54772 + 0.7303i + 0.18257j + 0.36515k ```

## Input Arguments

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Quaternion to normalize, specified as a scalar, vector, matrix, or multidimensional array of quaternions.

Data Types: `quaternion`

## Output Arguments

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Normalized quaternion, returned as a quaternion or array of quaternions the same size as `quat`.

Data Types: `quaternion`

## Version History

Introduced in R2020a