#### Archived

This topic is now archived and is closed to further replies.

This topic is 5491 days old which is more than the 365 day threshold we allow for new replies. Please post a new topic.

## Recommended Posts

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]

##### Share on other sites
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

##### Share on other sites
if you look at any physics 1 book on cross products

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

##### Share on other sites
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

1. 1
Rutin
32
2. 2
3. 3
4. 4
5. 5

• 11
• 13
• 87
• 11
• 10
• ### Forum Statistics

• Total Topics
632973
• Total Posts
3009617
• ### Who's Online (See full list)

There are no registered users currently online

×