As of May 4 2007 the scripts will autodetect your timezone settings. Nothing here has to be changed, but there are a few things

Please follow this blog

Search this blog

Saturday, December 12, 2009

Real matrix representations of quaternions

The quaternions were invented in 1843 by Hamilton. There are three quaternions: i, j and k where i is the well known imaginary number i. The rules for the multiplication of quaternions are as follows :

i * j = k, j * i = -k
j * k = i, k * j = -i
k * i = j, i * k = -j
i^2 = j^2 = k^2 = -1.

The quaternion group has eight members { 1, -1, i, j, k, -i, -j, -k } and is non-abelian.

The most common presentation of Q8 is < a,b | a^4 = 1, a^2 = b^2, b^-1*a*b = a^-1 >.

Using only real numbers the quaternions can be represented as 4-by-4 matrices as follows.

No comments:

Post a Comment

Popular Posts

Welcome to The Bridge

Mathematics: is it the fabric of MEST?
This is my voyage
My continuous mission
To uncover hidden structures
To create new theorems and proofs
To boldly go where no man has gone before

(Raumpatrouille – Die phantastischen Abenteuer des Raumschiffes Orion, colloquially aka Raumpatrouille Orion was the first German science fiction television series. Its seven episodes were broadcast by ARD beginning September 17, 1966. The series has since acquired cult status in Germany. Broadcast six years before Star Trek first aired in West Germany (in 1972), it became a huge success.)