1. the identity i<sup>2</sup>=j<sup>2</sup>=k<sup>2</sup>=ijk=-1

what i don't understand is the ijk part.

what i understand of it is that since quaternions are not commutative this part of the identity affects the results of quaternion multiplication but...
since i=j=k= square root (-1)
then shouldn't ijk=-i=-j=-k?

i'm obviously missing something here but i can't find what.  2.

3. i^2, j^2 and k^2 do equal -1, but i doesn't equal j, etc. (They're three different square roots. Another system [octonians, if I spelled it right] has 7.) The ijk=-1 is just part of (one of) the definition. (i*j)*k = k*k = -1. Also, i*(j*k) = i*i = -1.  4. Originally Posted by MagiMaster
i^2, j^2 and k^2 do equal -1, but i doesn't equal j, etc. (They're three different square roots. Another system [octonians, if I spelled it right] has 7.) The ijk=-1 is just part of (one of) the definition. (i*j)*k = k*k = -1. Also, i*(j*k) = i*i = -1.
ahh i see it now.

thank you.  Bookmarks
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