reflexive non-degenerate sesquilinear

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

$$v⟂w\text{ if and only if }w⟂v.$$

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