Phrase guide

Pauli matrix

noun · 1 senses · updated from the 2026-07-25 local source snapshot

Definitions and examples are grouped by meaning. Pronunciation, history, word forms, translations, descendants, synonyms, antonyms, derived terms, and related words appear whenever the source provides them.

Sound

Pronunciation

Each Play button uses your device's default local English voice, or a natural local fallback. The selected voice name appears after playback. This is synthesized speech, not a source recording.

No pronunciation record was provided for this word.

1

noun

Meaning 1

Any one of three complex matrices that arise in Wolfgang Pauli's treatment of spin in quantum mechanics.

Definition source: English Wiktionary via Wiktextract

Topics: mathematics, sciences

Examples

  • The Pauli matrices satisfy the equation #92;sigma#95;12#61;#92;sigma#95;22#61;#92;sigma#95;32#61;-i#92;sigma#95;1#92;sigma#95;2#92;sigma#95;3#61;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).
  • The eigenspinors are eigenvectors of the Pauli matrices in the case of a single spin 1/2 particle. —Wikipedia

Meaning relationships

Synonyms: none provided

Antonyms: none provided

History

Etymology

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

Across languages

Translations

4 source translations are retained for this English entry.

  • German: Pauli-Matrix — complex matrix
  • Polish: macierz Pauliego — complex matrix
  • Russian: ма́трица Па́ули (mátrica Páuli) — complex matrix
  • Swedish: Paulimatris — complex matrix