"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": "English entries with language name categories using raw markup",
          "parents": [
            "Entries with language name categories using raw markup",
            "Entry maintenance"
          ],
          "source": "w"
        },
        {
          "kind": "other",
          "name": "English terms with non-redundant non-automated sortkeys",
          "parents": [
            "Terms with non-redundant non-automated sortkeys",
            "Entry maintenance"
          ],
          "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 entries with language name categories using raw markup",
        "English eponyms",
        "English lemmas",
        "English multiword terms",
        "English nouns",
        "English terms with non-redundant non-automated sortkeys",
        "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"
}