Crossbones+ - Reputation: 2256
Posted 29 August 2012 - 09:14 PM
I was learning about quaternions the other day and I noticed something interesting about quaternion multiplication.
The component-wise form of Q3=Q1*Q2 is
w3=w1*w2 - v1.v2
v3 = v1*w2 + v2*w1 + v1Xv2
I noticed it looked very similar to a simple algebraic expansion of the form (a + b)(c + d).
Well if you look at the multiplication as a multiplication of their components you get:
(w1 + v1)(w2 + v2) = w1*w2 + w1*v2 + w2*v1 + (v1)(v2)
If you cancel terms from the first set of equations:
(v1)(v2) = v1Xv2 - v1.v2
What type of multiplication is this?
I'm sorry about any spelling or grammar mistakes or any undue brevity, as I'm most likely typing on my phone
"Hell, there's more evidence that we are just living in a frequency wave that flows in harmonic balance creating the universe and all its existence." ~ GDchat
Crossbones+ - Reputation: 2042
Posted 30 August 2012 - 03:23 AM