For more information about double numbers see this page.
Double Numbers over the real numbers are a 'field' they have the following properties:
|distributive over addition||-||yes|
As an Extension Field to Real Numbers
As a Multiplicative Group
If we ignore addition and treat complex numbers as a group then the group is equivalent to a D(2), it has the following properties:
The Cayley table is symmetric about its leading diagonal:
For more information about Cayley table see this page.
For more information about Cayley graph see this page.
The group has two generators each cycling between two elements:
For more information about cyclic notation see this page.
There is only one generator which when applied n times cycles back to the identity.
<a,b | a²=1,b²=1,ab=ba>
For more information about group presentation see this page.
A representation using 4 ×4 matricies containing 0 and 1 is:
An alternative 2×2 matrix representation containing 0, 1 and -1 is:
For more information about group representation see this page.