"pseudoreflection" meaning in English

{
  "etymology_templates": [
    {
      "args": {
        "1": "en",
        "2": "pseudo",
        "3": "reflection"
      },
      "expansion": "pseudo- + reflection",
      "name": "prefix"
    }
  ],
  "etymology_text": "From pseudo- + reflection.",
  "forms": [
    {
      "form": "pseudoreflections",
      "tags": [
        "plural"
      ]
    }
  ],
  "head_templates": [
    {
      "args": {},
      "expansion": "pseudoreflection (plural pseudoreflections)",
      "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 terms prefixed with pseudo-",
          "parents": [],
          "source": "w"
        },
        {
          "kind": "other",
          "name": "Pages with 1 entry",
          "parents": [],
          "source": "w"
        },
        {
          "kind": "other",
          "name": "Pages with entries",
          "parents": [],
          "source": "w"
        },
        {
          "kind": "topical",
          "langcode": "en",
          "name": "Mathematics",
          "orig": "en:Mathematics",
          "parents": [
            "Formal sciences",
            "Sciences",
            "All topics",
            "Fundamental"
          ],
          "source": "w"
        }
      ],
      "examples": [
        {
          "ref": "1967, A Background (natural, Synthetic and Algebraic) to Geometry, CUP Archive, page 293:",
          "text": "That is, t′x+y=0 is the pseudo-reflection of tx+y=0 if the ideal points (ρ′,1,0),(ρ,1,0) on the lines are a pair in the involution ρρ′=-h.",
          "type": "quote"
        },
        {
          "ref": "1985, Susan Montgomery, Group Actions on Rings, American Mathematical Soc., page 104:",
          "text": "A linear transformation g∈BL(V) is a pseudoreflection if rank (g-I)=1.",
          "type": "quote"
        },
        {
          "ref": "2009 January 9, Nicholas M. Katz, Twisted L-Functions and Monodromy, Princeton University Press, page 23:",
          "text": "It will be convenient to introduce two generalizations of the notion of pseudoreflection.",
          "type": "quote"
        }
      ],
      "glosses": [
        "An invertible linear transformation of a finite-dimensional vector space such that it is not the identity transformation, has a finite (multiplicative) order, and fixes a hyperplane."
      ],
      "id": "en-pseudoreflection-en-noun-Xlb98IiE",
      "links": [
        [
          "mathematics",
          "mathematics"
        ]
      ],
      "raw_glosses": [
        "(mathematics) An invertible linear transformation of a finite-dimensional vector space such that it is not the identity transformation, has a finite (multiplicative) order, and fixes a hyperplane."
      ],
      "topics": [
        "mathematics",
        "sciences"
      ],
      "wikipedia": [
        "pseudoreflection"
      ]
    }
  ],
  "word": "pseudoreflection"
}

{
  "etymology_templates": [
    {
      "args": {
        "1": "en",
        "2": "pseudo",
        "3": "reflection"
      },
      "expansion": "pseudo- + reflection",
      "name": "prefix"
    }
  ],
  "etymology_text": "From pseudo- + reflection.",
  "forms": [
    {
      "form": "pseudoreflections",
      "tags": [
        "plural"
      ]
    }
  ],
  "head_templates": [
    {
      "args": {},
      "expansion": "pseudoreflection (plural pseudoreflections)",
      "name": "en-noun"
    }
  ],
  "lang": "English",
  "lang_code": "en",
  "pos": "noun",
  "senses": [
    {
      "categories": [
        "English countable nouns",
        "English entries with incorrect language header",
        "English lemmas",
        "English nouns",
        "English terms prefixed with pseudo-",
        "English terms with quotations",
        "Pages with 1 entry",
        "Pages with entries",
        "en:Mathematics"
      ],
      "examples": [
        {
          "ref": "1967, A Background (natural, Synthetic and Algebraic) to Geometry, CUP Archive, page 293:",
          "text": "That is, t′x+y=0 is the pseudo-reflection of tx+y=0 if the ideal points (ρ′,1,0),(ρ,1,0) on the lines are a pair in the involution ρρ′=-h.",
          "type": "quote"
        },
        {
          "ref": "1985, Susan Montgomery, Group Actions on Rings, American Mathematical Soc., page 104:",
          "text": "A linear transformation g∈BL(V) is a pseudoreflection if rank (g-I)=1.",
          "type": "quote"
        },
        {
          "ref": "2009 January 9, Nicholas M. Katz, Twisted L-Functions and Monodromy, Princeton University Press, page 23:",
          "text": "It will be convenient to introduce two generalizations of the notion of pseudoreflection.",
          "type": "quote"
        }
      ],
      "glosses": [
        "An invertible linear transformation of a finite-dimensional vector space such that it is not the identity transformation, has a finite (multiplicative) order, and fixes a hyperplane."
      ],
      "links": [
        [
          "mathematics",
          "mathematics"
        ]
      ],
      "raw_glosses": [
        "(mathematics) An invertible linear transformation of a finite-dimensional vector space such that it is not the identity transformation, has a finite (multiplicative) order, and fixes a hyperplane."
      ],
      "topics": [
        "mathematics",
        "sciences"
      ],
      "wikipedia": [
        "pseudoreflection"
      ]
    }
  ],
  "word": "pseudoreflection"
}