What in the world is a Quaternion and how do I understand IT?
Throw me everything you know about it.
In: Mathematics
Most basically, a quaternion is what you get if you ask ‘what if there were three imaginary numbers?’
With 1 imaginary number, you get the result i²=-1
With 3 imaginary numbers, you still get i²=-1, but you also get j²=-1 and k²=-1
Furthermore, the imaginary numbers multiply to get each other:
i*j=k, j*k=i, k*i=j. However, multiplication is no longer commutative, meaning that multiplying in a different order gives you a different value: j*i=-k, k*j=-i, i*k=-j
A Quaternion has components, the real component and 3 imaginary ones.
Quaternions have been used as an alternative to vectors. You can represent a vector as a purely imaginary quaternion by putting the x component in front of the i, y component in front of the j, and z component in front of the k (This is why, for example, you often see vectors as having i,j, and k components instead of x,y,z), then multiplying two such quaternions will give you the dot product of those two vectors in the real term, and the cross product in the imaginary term.
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