"pseudoreflection" meaning in English

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          "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.",
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          "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.",
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        "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."
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        "(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."
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        "mathematics",
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          "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.",
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