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Quaternion

Numbers with four dimensions are called quaternions. You write them as

x =  x0 e0 +  x1 e1 +  x2 e2 +  x3 e3

and consists of the real numbers xa and the units

{ e0 ,  e1 ,  e2 ,  e3 }

The unit e0 is the real number 1.

 


Explanation

When multiplying the units e0 , e1 , e2 , e3 } the order plays a role.

× e0 e1 e2
e0 e0 e1 e2
e1 e1 e0 e3
e2 e2 −e3 e0

Quaternions can therefore be used to describe a rotation in three dimensions. A point (x1x2x3) in three dimensions forms the imaginary part x1e1x2e2x3e3 of a quaternion.

 


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