# reflexive non-degenerate sesquilinear

A non-degenerate sesquilinear form $b:V\times V\rightarrow k$ is reflexive if for all $v,w\in V$, if $b(v,w)=0$ then $b(w,v)=0$. This means

 $v\perp w\textnormal{ if and only if }w\perp v.$

It is rare to define perpendicularity for sesquilinear/bilinear maps which are not reflexive because it would require a version of left and right perpendicular. Thus a reflexive sesquilinear/bilinear map is usually synonymous with the existence of perpendicularity.

 Title reflexive non-degenerate sesquilinear Canonical name ReflexiveNondegenerateSesquilinear Date of creation 2013-03-22 15:51:04 Last modified on 2013-03-22 15:51:04 Owner Algeboy (12884) Last modified by Algeboy (12884) Numerical id 10 Author Algeboy (12884) Entry type Definition Classification msc 15A63 Synonym reflexive non-degenerate bilinear Synonym reflexive sesquilinear Synonym reflexive bilinear Related topic SesquilinearFormsOverGeneralFields Defines Reflexive non-degenerate sesquilinear Defines Reflexive non-degenerate bilinear Defines Reflexive