Quaternion Group - Cayley Table

Cayley Table

The Cayley table (multiplication table) for Q is given by:

	1	−1	i	−i	j	−j	k	−k
1	1	−1	i	−i	j	−j	k	−k
−1	−1	1	−i	i	−j	j	−k	k
i	i	−i	−1	1	k	−k	−j	j
−i	−i	i	1	−1	−k	k	j	−j
j	j	−j	−k	k	−1	1	i	−i
−j	−j	j	k	−k	1	−1	−i	i
k	k	−k	j	−j	−i	i	−1	1
−k	−k	k	−j	j	i	−i	1	−1

The multiplication of pairs of elements from the subset {±i, ±j, ±k} works like the cross product of unit vectors in three-dimensional Euclidean space.

$\begin{alignat}{2} ij & = k, & ji & = -k, \\ jk & = i, & kj & = -i, \\ ki & = j, & ik & = -j. \end{alignat}$

Read more about this topic: Quaternion Group

Famous quotes containing the word table:

“But hospitality must be for service, and not for show, or it pulls down the host. The brave soul rates itself too high to value itself by the splendor of its table and draperies. It gives what it hath, and all it hath, but its own majesty can lend a better grace to bannocks and fair water than belong to city feasts.”
—Ralph Waldo Emerson (1803–1882)