Difference between revisions of "Pure and unit quaternions"
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{{Navigation|before=[[Basic properties of quaternions]]|overview=[[Quaternions]]|next=[[Addition of quaternions]]}} | {{Navigation|before=[[Basic properties of quaternions]]|overview=[[Quaternions]]|next=[[Addition of quaternions]]}} | ||
| + | __NOTOC__ | ||
| + | ===Pure quaternion=== | ||
| + | A quaternion whose vector part is zero equals a real number corresponding to the scalar part. | ||
| + | |||
| + | A quaternion whose scalar part | ||
| + | :<math> | ||
| + | i^2 = j^2 = k^2 = ijk = -1 | ||
| + | </math> | ||
| + | Unlike the multiplication of real or complex numbers, the multiplication is not commutative: | ||
| + | :<math> | ||
| + | \begin{align} | ||
| + | ij &= -ji = k \\ | ||
| + | jk &= -kj = i \\ | ||
| + | ki &= -ik = j | ||
| + | \end{align} | ||
| + | </math> | ||
Revision as of 15:25, 23 June 2015
| ← Back: Basic properties of quaternions | Overview: Quaternions | Next: Addition of quaternions → |
Pure quaternion
A quaternion whose vector part is zero equals a real number corresponding to the scalar part.
A quaternion whose scalar part
Unlike the multiplication of real or complex numbers, the multiplication is not commutative:
