# quatnormalize

Normalize quaternion

## Syntax

`n = quatnormalize(q)`

## Description

`n = quatnormalize(q)` calculates the normalized quaternion, `n`, for a given quaternion, `q`. Input `q` is an `m`-by-4 matrix containing `m` quaternions. `n` returns an `m`-by-4 matrix of normalized quaternions. Each element of `q` must be a real number. Additionally, `q` has its scalar number as the first column.

The quaternion has the form of

$q={q}_{0}+i{q}_{1}+j{q}_{2}+k{q}_{3}$

The normalized quaternion has the form of

$normal\left(q\right)=\frac{{q}_{0}+i{q}_{1}+j{q}_{2}+k{q}_{3}}{\sqrt{{q}_{0}^{2}+{q}_{1}^{2}+{q}_{2}^{2}+{q}_{3}^{2}}}$

## Examples

Normalize `q = [1 0 1 0]`:

```normal = quatnormalize([1 0 1 0]) normal = 0.7071 0 0.7071 0```

## References

[1] Stevens, Brian L., Frank L. Lewis, Aircraft Control and Simulation, Wiley–Interscience, 2nd Edition.