The split-quaternions are an algebra over the real numbers. Every split quaternion may be represented as
where the basis elements satisfy the following products:
i | j | k | |
---|---|---|---|
i | -1 | k | -j |
j | -k | +1 | -i |
k | j | i | +1 |
and conjugation .
These are closely related to the quaternions, as the generators satisfy similarly-looking relations. They are obtained from the split-complex numbers through the generalization of the Cayley-Dickson construction.
See also
On projective spaces over split-quaternions:
Last revised on November 3, 2023 at 05:16:33. See the history of this page for a list of all contributions to it.