reflexive non-degenerate sesquilinearReflexiveNonDegenerateSesquilinear2006-04-14 19:28:372006-09-06 11:11:41DefinitionReflexive non-degenerate sesquilinearReflexive non-degenerate bilinearReflexiveReflexive\usepackage{latexsym}
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\providecommand{\bigintersect}{\bigcap}A non-degenerate sesquilinear form $b:V\times V\rightarrow k$ is \emph{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.