Question about Hamilton's Quaternion Paper

Question

So I was reading Hamilton's paper on quaternions. http://www.emis.de/classics/Hamilton/OnQuat.pdf. On page 2, I'm having trouble following how QQ' and equations A,B,C lead to equation D. My main question is in the original expression for QQ', we have terms like iwx' and jyw'. Basically, I don't see how those i's and j's disappeared in equation D, and why logically we arrange all the terms like that.

Thanks

score 1 · Accepted Answer · answered Nov 18 '14 at 08:42

1

They don't disappear; what you see is components of the new quaternion $$ Q''=w''+ix''+iy''+iz''=QQ' $$

answered Nov 18 '14 at 08:42

Troy Woo

3,579

What's the logic for the grouping then in equation D? – Gakho Nov 18 '14 at 09:15
@GabrielKho What is then the logic for the grouping of real parts and imaginary parts when you multiply two complex numbers? – Troy Woo Nov 18 '14 at 09:27
Well, I mean take x'' for example, the last two terms are yz' and zy'. I don't see how those got assigned there. – Gakho Nov 18 '14 at 09:29
@GabrielKho $jk=-kj=i$. – Troy Woo Nov 18 '14 at 09:40

Question about Hamilton's Quaternion Paper

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