"Pauli matrix" meaning in All languages combined

{
  "etymology_text": "Named after Wolfgang Ernst Pauli (1900–1958), Austrian theoretical physicist.",
  "forms": [
    {
      "form": "Pauli matrixes",
      "tags": [
        "plural"
      ]
    },
    {
      "form": "Pauli matrices",
      "tags": [
        "plural"
      ]
    }
  ],
  "head_templates": [
    {
      "args": {
        "1": "+",
        "2": "Pauli matrices",
        "head": "Pauli matrix"
      },
      "expansion": "Pauli matrix (plural Pauli matrixes or Pauli matrices)",
      "name": "en-noun"
    }
  ],
  "lang": "English",
  "lang_code": "en",
  "pos": "noun",
  "senses": [
    {
      "categories": [
        {
          "kind": "other",
          "name": "English entries with incorrect language header",
          "parents": [
            "Entries with incorrect language header",
            "Entry maintenance"
          ],
          "source": "w"
        },
        {
          "kind": "other",
          "name": "Entries with translation boxes",
          "parents": [],
          "source": "w"
        },
        {
          "kind": "other",
          "name": "Pages with 1 entry",
          "parents": [],
          "source": "w"
        },
        {
          "kind": "other",
          "name": "Pages with entries",
          "parents": [],
          "source": "w"
        },
        {
          "kind": "other",
          "name": "Terms with German translations",
          "parents": [],
          "source": "w"
        },
        {
          "kind": "other",
          "name": "Terms with Russian translations",
          "parents": [],
          "source": "w"
        },
        {
          "kind": "other",
          "name": "Terms with Swedish translations",
          "parents": [],
          "source": "w"
        },
        {
          "kind": "topical",
          "langcode": "en",
          "name": "Mathematics",
          "orig": "en:Mathematics",
          "parents": [
            "Formal sciences",
            "Sciences",
            "All topics",
            "Fundamental"
          ],
          "source": "w"
        }
      ],
      "examples": [
        {
          "text": "The Pauli matrices satisfy the equation σ₁²=σ₂²=σ₃²=-iσ₁σ₂σ₃=I which is reminiscent of Hamilton's fundamental formula for quaternion multiplication."
        },
        {
          "text": "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)."
        },
        {
          "text": "The eigenspinors are eigenvectors of the Pauli matrices in the case of a single spin 1/2 particle. —Wikipedia"
        }
      ],
      "glosses": [
        "Any one of three complex matrices that arise in Wolfgang Pauli's treatment of spin in quantum mechanics."
      ],
      "holonyms": [
        {
          "word": "Pauli vector"
        }
      ],
      "hypernyms": [
        {
          "word": "Hermitian matrix"
        },
        {
          "word": "unitary matrix"
        }
      ],
      "id": "en-Pauli_matrix-en-noun-mhy42N8F",
      "links": [
        [
          "mathematics",
          "mathematics"
        ],
        [
          "complex",
          "complex"
        ],
        [
          "spin",
          "spin"
        ],
        [
          "quantum mechanics",
          "quantum mechanics"
        ]
      ],
      "raw_glosses": [
        "(mathematics) Any one of three complex matrices that arise in Wolfgang Pauli's treatment of spin in quantum mechanics."
      ],
      "topics": [
        "mathematics",
        "sciences"
      ],
      "translations": [
        {
          "code": "de",
          "lang": "German",
          "sense": "complex matrix",
          "tags": [
            "feminine"
          ],
          "word": "Pauli-Matrix"
        },
        {
          "code": "ru",
          "lang": "Russian",
          "roman": "mátrica Páuli",
          "sense": "complex matrix",
          "tags": [
            "feminine"
          ],
          "word": "ма́трица Па́ули"
        },
        {
          "code": "sv",
          "lang": "Swedish",
          "sense": "complex matrix",
          "tags": [
            "common-gender"
          ],
          "word": "Paulimatris"
        }
      ],
      "wikipedia": [
        "Pauli matrices",
        "Wolfgang Ernst Pauli"
      ]
    }
  ],
  "word": "Pauli matrix"
}

{
  "etymology_text": "Named after Wolfgang Ernst Pauli (1900–1958), Austrian theoretical physicist.",
  "forms": [
    {
      "form": "Pauli matrixes",
      "tags": [
        "plural"
      ]
    },
    {
      "form": "Pauli matrices",
      "tags": [
        "plural"
      ]
    }
  ],
  "head_templates": [
    {
      "args": {
        "1": "+",
        "2": "Pauli matrices",
        "head": "Pauli matrix"
      },
      "expansion": "Pauli matrix (plural Pauli matrixes or Pauli matrices)",
      "name": "en-noun"
    }
  ],
  "holonyms": [
    {
      "word": "Pauli vector"
    }
  ],
  "hypernyms": [
    {
      "word": "Hermitian matrix"
    },
    {
      "word": "unitary matrix"
    }
  ],
  "lang": "English",
  "lang_code": "en",
  "pos": "noun",
  "senses": [
    {
      "categories": [
        "English countable nouns",
        "English entries with incorrect language header",
        "English eponyms",
        "English lemmas",
        "English multiword terms",
        "English nouns",
        "Entries with translation boxes",
        "Pages with 1 entry",
        "Pages with entries",
        "Terms with German translations",
        "Terms with Russian translations",
        "Terms with Swedish translations",
        "en:Mathematics"
      ],
      "examples": [
        {
          "text": "The Pauli matrices satisfy the equation σ₁²=σ₂²=σ₃²=-iσ₁σ₂σ₃=I which is reminiscent of Hamilton's fundamental formula for quaternion multiplication."
        },
        {
          "text": "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)."
        },
        {
          "text": "The eigenspinors are eigenvectors of the Pauli matrices in the case of a single spin 1/2 particle. —Wikipedia"
        }
      ],
      "glosses": [
        "Any one of three complex matrices that arise in Wolfgang Pauli's treatment of spin in quantum mechanics."
      ],
      "links": [
        [
          "mathematics",
          "mathematics"
        ],
        [
          "complex",
          "complex"
        ],
        [
          "spin",
          "spin"
        ],
        [
          "quantum mechanics",
          "quantum mechanics"
        ]
      ],
      "raw_glosses": [
        "(mathematics) Any one of three complex matrices that arise in Wolfgang Pauli's treatment of spin in quantum mechanics."
      ],
      "topics": [
        "mathematics",
        "sciences"
      ],
      "wikipedia": [
        "Pauli matrices",
        "Wolfgang Ernst Pauli"
      ]
    }
  ],
  "translations": [
    {
      "code": "de",
      "lang": "German",
      "sense": "complex matrix",
      "tags": [
        "feminine"
      ],
      "word": "Pauli-Matrix"
    },
    {
      "code": "ru",
      "lang": "Russian",
      "roman": "mátrica Páuli",
      "sense": "complex matrix",
      "tags": [
        "feminine"
      ],
      "word": "ма́трица Па́ули"
    },
    {
      "code": "sv",
      "lang": "Swedish",
      "sense": "complex matrix",
      "tags": [
        "common-gender"
      ],
      "word": "Paulimatris"
    }
  ],
  "word": "Pauli matrix"
}