Dictionary

pseudoreflection en · NOUN

Pronunciation

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Etymology

From pseudo- + reflection.

Meanings

1. 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.
   • A linear transformation g∈BL(V) is a pseudoreflection if rank (g-I)=1. 1985, Susan Montgomery, Group Actions on Rings, American Mathematical Soc., page 104:
   • 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. 1967, A Background (natural, Synthetic and Algebraic) to Geometry, CUP Archive, page 293:
   • It will be convenient to introduce two generalizations of the notion of pseudoreflection. 2009 January 9, Nicholas M. Katz, Twisted L-Functions and Monodromy, Princeton University Press, page 23:

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