PlanetMath: reflexive non-degenerate sesquilinear

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reflexive non-degenerate sesquilinear

(Definition)

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

$% latex2html id marker 331 $\displaystyle 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.

"reflexive non-degenerate sesquilinear" is owned by Algeboy.

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Other names:

reflexive non-degenerate bilinear, reflexive sesquilinear, reflexive bilinear

Also defines:

Reflexive non-degenerate sesquilinear, Reflexive non-degenerate bilinear, Reflexive

Keywords:

Reflexive

Attachments:: left / right perpendicular (Derivation) by Algeboy

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Cross-references: right perpendicular, maps, perpendicularity, sesquilinear form, non-degenerate
There are 39 references to this entry.

This is version 7 of reflexive non-degenerate sesquilinear, born on 2006-04-14, modified 2006-09-06.
Object id is 7834, canonical name is ReflexiveNonDegenerateSesquilinear.
Accessed 4881 times total.

Classification:

AMS MSC:

15A63 (Linear and multilinear algebra; matrix theory :: Quadratic and bilinear forms, inner products)

Pending Errata and Addenda

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