Pauli matrices
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In mathematical physics and mathematics, the Pauli matrices are a set of three 2 × 2 complex matrices that are traceless, Hermitian, involutory and unitary. They are usually denoted by the Greek lette
Wolfgang Pauli (1900–1958), c. 1924. Pauli received the Nobel Prize in Physics in 1945, nominated by Albert Einstein, for the Pauli exclusion principle.
Quaternion
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In mathematics, the quaternions form a number system similar to the complex numbers, with the usual arithmetical operations of addition, subtraction, multiplication, and division, but with four real-n
Pauli matrices
…Clifford algebra of R 3 and the (unital) associative algebra generated by i σ 1 , i σ 2 , and i σ 3 functions identically (is isomorphic) to that of quaternions ( H ). All three of the Pauli matrices can be compacted into a single expression…
Quaternion plaque on Brougham (Broom) Bridge, Dublin, which reads: Here as he walked by on the 16th of October 1843 Sir William Rowan Hamilton in a flash of genius discovered the fundamental formula for quaternion multiplication i2 = j2 = k2 = i j k = −1 & cut it on a stone of this bridge
The Julia sets and Mandelbrot sets can be extended to the Quaternions, but they must use cross sections to be rendered visually in 3 dimensions. This Julia set is cross sectioned at the x y plane.