# Pauli matrix

## English

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### Etymology

Named after Wolfgang Ernst Pauli (1900–1958), Austrian theoretical physicist.

### Noun

Pauli matrix ‎(plural Pauli matrixes or Pauli matrices)

1. (mathematics) Any one of three complex matrices that arise in Wolfgang Pauli's treatment of spin in quantum mechanics.
The Pauli matrices satisfy the equation ${\displaystyle \sigma _{1}^{2}=\sigma _{2}^{2}=\sigma _{3}^{2}=-i\sigma _{1}\sigma _{2}\sigma _{3}=I}$ which is reminiscent of Hamilton's fundamental formula for quaternion multiplication.
The first Pauli matrix is like a reflection about the "y=x" line. The third Pauli matrix is like a reflection about the "x axis". The second Pauli matrix is like a 90° counterclockwise rotation and scalar multiplication by the imaginary unit (which rotates the two complex components by 90° counterclockwise in their own "phasor spaces", as it were).