Quaternion

+Quaternion multiplication table 

In mathematics, the quaternion number system (represented using the symbol ) extends the complex numbers into four dimensions. They were first described by Irish mathematician William Rowan Hamilton in 1843. They are often used in computer graphics to compute 3-dimensional rotations.

The eight-dimensional octonions come after the quaternions.

 Definition 
A quaternion is a number written like this:

where  are real numbers, and  are the symbols called imaginary units.

 Multiplication 
The square of every imaginary unit is equal to -1

When you multiply, changing the order of the numbers can give a different answer.



Putting all those together,

References

Other websites

 Paulson, Lawrence C. Quaternions (Formal proof development in Isabelle/HOL, Archive of Formal Proofs) 
 Quaternions – Visualisation

Category:algebra
Category:Numbers