The Pauli matrices satisfy the equation 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).
Origin of pauli-matrix
- Named after Wolfgang Ernst Pauli (1900–1958), Austrian theoretical physicist.