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Historical Roots, II<br />
William Rowan Hamilton (1805-65)<br />
inv<strong>en</strong>ts Quaternions (1844):<br />
– G<strong>en</strong>eralization of complex numbers:<br />
• 4 compon<strong>en</strong>ts, non commutative: ab ba<br />
(in g<strong>en</strong>eral)<br />
• Basic idea: ii=jj=kk= ijk = -1<br />
• Alternative to younger vector- and matrix<br />
algebra (Josiah Willard Gibbs, 1839-1903)<br />
• p=(p,p), q=(q,q), p q=(pq - p q , pq + pq<br />
+ p q)<br />
• rotation in R 3 are around axis of the vector<br />
compon<strong>en</strong>t: v’ = q v q -1<br />
6
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