# Documentation

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# quatconj

Calculate conjugate of quaternion

## Syntax

`n = quatconj(q)`

## Description

`n = quatconj(q)` calculates the conjugate, `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 conjugates. 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 quaternion conjugate has the form of

`${q}^{\prime }={q}_{0}-i{q}_{1}-j{q}_{2}-k{q}_{3}$`

## Examples

Determine the conjugate of `q = [1 0 1 0]`:

```conj = quatconj([1 0 1 0]) conj = 1 0 -1 0```

## References

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