# Maths - Pauli matrices - 2D

The basis vectors can be represented by matrices, this algebra was worked out independently by Pauli for his work on quantum mechanics, we can define the following equivalents:

e1=
 0 1 1 0
e2=
 1 0 0 -1

The scalar would be the identity matrix.

1=
 1 0 0 1

The bivector can be calculated by multiplying the matrices:

e1e2=
 0 1 1 0
*
 1 0 0 -1
=
 0 -1 1 0

So the complete geometric multiplication table is:

a*b
b.e b.e1 b.e2 b.e12
a.e
 1 0 0 1
 0 1 1 0
 1 0 0 -1
 0 -1 1 0
a.e1
 0 1 1 0
 1 0 0 1
 0 -1 1 0
 1 0 0 -1
a.e2
 1 0 0 -1
 0 1 -1 0
 1 0 0 1
 0 -1 -1 0
a.e12
 0 -1 1 0
 -1 0 0 1
 0 1 1 0
 -1 0 0 -1

which is equivilant to the table derived here.

Any multivector can be represented by a single matrix representing a linear sum of these basis, for instance,

 4 3 3 -4
= 3*
 0 1 1 0
+ 4*
 1 0 0 -1
= 3e1+ 4e2

Other uses of Pauli Matrix:

Related Concepts:

Where I can, I have put links to Amazon for books that are relevant to the subject, click on the appropriate country flag to get more details of the book or to buy it from them.

 Geometric Algebra for Physicists - This is intended for physicists so it soon gets onto relativity, spacetime, electrodynamcs, quantum theory, etc. However the introduction to Geometric Algebra and classical mechanics is useful.