pseudoreflection

English

Etymology

From pseudo- +‎ reflection.

Noun

pseudoreflection (plural pseudoreflections)

1. (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.
   • 1967, A Background (natural, Synthetic and Algebraic) to Geometry, CUP Archive, page 293:

     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.

   • 1985, Susan Montgomery, Group Actions on Rings, American Mathematical Soc., page 104:

     A linear transformation g∈BL(V) is a pseudoreflection if rank (g-I)=1.

   • 2009 January 9, Nicholas M. Katz, Twisted L-Functions and Monodromy, Princeton University Press, page 23:

     It will be convenient to introduce two generalizations of the notion of pseudoreflection.