# Pauli spin matrices

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*20 December 2010*.The **Pauli spin matrices** (named after physicist Wolfgang Ernst Pauli) are a set of unitary Hermitian matrices which form an orthogonal basis (along with the identity matrix) for the real Hilbert space of 2 × 2 Hermitian matrices and for the complex Hilbert spaces of all 2 × 2 matrices. They are usually denoted:

## [edit] Algebraic properties

For *i* = 1, 2, 3:

### [edit] Commutation relations

The Pauli matrices obey the following commutation and anticommutation relations:

- where is the Levi-Civita symbol, δ
_{ij}is the Kronecker delta, and I is the identity matrix.

The above two relations can be summarized as:

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