## Pauli Matrices

Matrices which arise in Pauli's treatment of spin in quantum mechanics. They are defined by

 (1) (2) (3)

The Pauli matrices plus the Identity Matrix I form a complete set, so any matrix A can be expressed as
 (4)

The associated matrices

 (5) (6) (7)

can also be defined. The Pauli spin matrices satisfy the identities
 (8)

 (9)

 (10)

Goldstein, H. The Cayley-Klein Parameters and Related Quantities.'' Classical Mechanics, 2nd ed. Reading, MA: Addison-Wesley, p. 156, 1980.