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Pauli matrices

The Pauli matrices are a set of traceless involutive hermitian matrices with a number of nice properties

Notably these form a basis for the real vector space , and with the addition of , they form a basis for the complex vector space .

Properties

Here we use Einstein summation convention.

1. Linear commutator: with Levi-Civita symbol
2. Matrix anticommutator:
3. Product:

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