Q



Quaternion

The ring of quaternions, discovered by W.R. Hamilton provides the most often cited example of a skew field or division ring it consists of all possible sums of the form

a1 + bi + cj +dk

where a,b,c and d are real numbers and 1,i,j and k are members of the quaternionic group. For concreteness we can take 1,i,j and k to be 4 x 4 matrices:


1 =  1  0  0  0   i = 0 -1  0  0   j = 0  0 -1  0   k = 0  0  0 -1
     0  1  0  0       1  0  0  0       0  0  0  1       0  0 -1  0 
     0  0  1  0       0  0  0 -1       1  0  0  0       0  1  0  0
     0  0  0  1       0  0  1  0       0 -1  0  0       1  0  0  0


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An On-line Dictionary of Combinatorics