inverse

Quaternion.inverse

Return the inverse Quaternion

The inverse quaternion \(\mathbf{q}^{-1}\) is such that the quaternion times its inverse gives the identity quaternion \(\mathbf{q}_I=\begin{pmatrix}1 & 0 & 0 & 0\end{pmatrix}\)

It is obtained as:

\[\mathbf{q}^{-1} = \frac{\mathbf{q}^*}{\|\mathbf{q}\|^2}\]

If the quaternion is normalized (called versor) its inverse is the conjugate.

\[\mathbf{q}^{-1} = \mathbf{q}^*\]

Returns:

out – Inverse of quaternion.

Return type:

numpy.ndarray

Examples

>>> q = Quaternion([1., -2., 3., -4.])
>>> q
Quaternion([ 0.18257419, -0.36514837,  0.54772256, -0.73029674])
>>> q.inverse
array([ 0.18257419,  0.36514837, -0.54772256,  0.73029674])
>>> q@q.inverse
array([1.00000000e+00, 0.00000000e+00, 0.00000000e+00, 2.77555756e-17])