pseudoreflection

plural pseudoreflections

1. mathematicsAn 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

   2 more examples

   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