# quatmod

Calculate modulus of quaternion

## Syntax

``n = quatmod(q)``

## Description

example

````n = quatmod(q)` calculates the modulus `n` for a given quaternion, `q`. For more information on the quaternion and quaternion modulus forms, see Algorithms.Aerospace Toolbox uses quaternions that are defined using the scalar-first convention.```

## Examples

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Determine the modulus of q = [1 0 0 0].

`mod = quatmod([1 0 0 0])`
```mod = 1 ```

## Input Arguments

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Quaternion, specified in a m-by-4 matrix of real numbers containing m quaternions.

Example: `[1 0 0 0]`

Data Types: `double`

## Output Arguments

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Moduli, returned as a column vector of `m` elements.

## Algorithms

The quaternion has the form of

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

The quaternion modulus has the form of

`$|q|=\sqrt{{q}_{0}^{2}+{q}_{1}^{2}+{q}_{2}^{2}+{q}_{3}^{2}}.$`

 Stevens, Brian L. and Frank L. Lewis. Aircraft Control and Simulation. 2nd ed. Wiley–Interscience, 2003.