There is a funny history septernion that I will post about someday. Today I will talk Hamilton’s quaternions.  They are also called hyper complex numbers and can be summarized by the formula below, which by the way, is in a plate in a bridge in Dublin. Quaternios expression is:

q = 

The i, j and k part are the vector part, or imaginary.

 Properties

Multiplication is not COMMUTATIVE  – yes the first to be discovered.

ij=k           ji=−k

        jk=i           kj=−i  

         ki=j          ik=−j

 Forgot

Quaternions, as well as part of Hamilton’s work was forgot specially because of the utilization of vectors representation actually.

Revival

But recently quaternions were revived by describing spatial rotations! Yup! Forget vector representation haha.

  Suggestion

Well, my main suggestion if your interested is to learn it from [3], which explain with some details about quaternions for computer 3D graphic animation.

Ref

[1]https://en.wikipedia.org/wiki/Quaternion

[2] http://www.tfd.chalmers.se/~hani/kurser/OS_CFD_2008/ErikEkedahl/reportErikEkedahl.pdf

[3] https://www.3dgep.com/understanding-quaternions/