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Bile

Quaternions....please shed some insight!

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Hi all, I'm desperately trying to understand how quaternions work. So far, it's not so bad except one concept I can't seem to grasp. Check this out: According to this guy Hamilton's theory, hypercomplex numbers work according like this: ijk = 1 (although some internet sources say ijk=-1 and I can't figure out why!) based on this: ij = k jk = i ki = j ji = -k kj = -i ik = -j The question is: HOW can we derive that ij = k for example when I don't event know for sure whether ijk = 1 OR ijk = -1. Can anyone help me out here? Thanks a lot. [edited by - bile on October 8, 2003 12:50:07 PM]

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Guest Anonymous Poster
It goes like this:
i^2 = j^2 = k^2 = ijk = -1

ij = -ji = k

jk = -kj = i

ki = -ik = j

More can be found here: http://mathworld.wolfram.com/Quaternion.html

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if you look at any physics 1 book on cross products
you''ll find your answer there.

if i remember correctly the reason why ijk can equal 1 or -1 is dependent of the direction of the resultant vector.

if the resultant vector is 1 then you''re using the right hand rule. if it''s -1 then it''s the left hand rule.

i won''t lie though i know i''m missing some theory somewhere but i believe that''s the general jist of it

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I''m glad that I''m not the only one with a quaternion question

i, j, and k represent three perpendicular directions in hypercomplex space.

Normally just i is used to represent the square root of -1 but it turns out that you can also have j and k to represent the square root of -1 and all three are perpendicular in a higher dimensional space.

When you use a quaternion to represent a rotation the sign of the quaternion really doesn''t matter because q = -q. The size of the quaternion doesn''t even matter (q = aq for all a)

(the way to think of this is like a vector representing a direction where no matter what the length of the vector is it will always point along the same direction)

That probably didn''t answer your question but I thought I''d share what I''d learnt...

Fleejay

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