Pauli Matrices

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WIKIPEDIA articles! In physics, the Pauli matrices are a set of 2 × 2
complex Hermitian and unitary matrices (See also ref.[1]). Usually
indicated by the Greek letter 'sigma' (¿), they are occasionally denoted
with a 'tau' (¿) when used in connection with isospin symmetries. They
are: sigma_1 = sigma_x = begin{pmatrix} 0&1 1&0 end{pmatrix}
sigma_2 = sigma_y = begin{pmatrix} 0&-i i&0 end{pmatrix} sigma_3
= sigma_z = begin{pmatrix} 1&0 0&-1 end{pmatrix}. The name
refers to Wolfgang Pauli. The real (hence also, complex) subalgebra
generated by the ¿i (that is, the set of real or complex linear
combinations of all the elements which can be built up as products of
Pauli matrices) is the full set M2(C) of complex 2×2 matrices. The ¿i
can also be seen as generating the real Clifford algebra of the real
quadratic form with signature (3,0): this shows that this Clifford
algebra C¿3,0(R) is isomorphic to M2(C), with the Pauli matrices
providing an explicit isomorphism. (In particular, the Pauli matrices
define a faithful representation of the real Clifford algebra C¿3,0(R)
on the complex vector space C2 of dimension 2.)