Accelerating the pace of engineering and science

# quatinv

Calculate inverse of quaternion

n = quatinv(q)

## Description

n = quatinv(q) calculates the inverse, 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 inverses. 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 inverse has the form of

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

## Examples

Determine the inverse of q = [1 0 1 0]:

```qinv = quatinv([1 0 1 0])

qinv =

0.5000         0   -0.5000         0```

## References

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