Quaternion
noncommutative extension of the real numbers
| 1 | i | j | k | |
|---|---|---|---|---|
| 1 | 1 | i | j | k |
| i | i | −1 | k | −j |
| j | j | −k | −1 | i |
| k | k | j | −i | −1 |
In mathematics, the quaternion number system extends the complex numbers. They were first described by Irish mathematician William Rowan Hamilton in 1843.[1][2]
Cayley Q8 graph showing the 6 cycles of multiplication by i, j and k. (In the SVG file, hover over or click a cycle to highlight it.)
ReferencesEdit
- ↑ "On Quaternions; or on a new System of Imaginaries in Algebra". Letter to John T. Graves. 17 October 1843.
- ↑ Rozenfelʹd, Boris Abramovich (1988). The history of non-euclidean geometry: Evolution of the concept of a geometric space. Springer. p. 385. ISBN 9780387964584.
Other websitesEdit
| The English Wikibook Associative Composition Algebra has more information on: |
| Wikiquote has a collection of quotations related to: Quaternion |
Media related to Quaternions at Wikimedia Commons- Paulson, Lawrence C. Quaternions (Formal proof development in Isabelle/HOL, Archive of Formal Proofs)
- Quaternions – Visualisation
