Pauli matrix

Etymology
Named after (1900–1958), Austrian theoretical physicist.

Noun

 * 1)  Any one of three complex matrices that arise in Wolfgang Pauli's treatment of spin in quantum mechanics.
 * The Pauli matrices satisfy the equation $$\sigma_1^2 = \sigma_2^2 = \sigma_3^2 = -i\sigma_1 \sigma_2 \sigma_3 = I$$ 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&deg; counterclockwise rotation and scalar multiplication by the imaginary unit (which rotates the two complex components by 90&deg; counterclockwise in their own "phasor spaces", as it were).
 * The eigenspinors are eigenvectors of the Pauli matrices in the case of a single spin 1/2 particle. &mdash;

Translations

 * German: Pauli-Matrix
 * Russian: ма́трица Па́ули
 * Swedish: Paulimatris