reflexive non-degenerate sesquilinear

A non-degenerate sesquilinear formPlanetmathPlanetmath b:V×Vk is reflexiveMathworldPlanetmathPlanetmathPlanetmathPlanetmath if for all v,wV, if b(v,w)=0 then b(w,v)=0. This means

vw if and only if wv.

It is rare to define perpendicularityPlanetmathPlanetmath for sesquilinear/bilinear maps which are not reflexive because it would require a version of left and right perpendicularMathworldPlanetmath. 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