left / right perpendicular

Given a sesquilinear formPlanetmathPlanetmath b:V×Vk over the field k, if v,uV such that b(v,u)=0 then we say v is right perpendicular to u and denote it vu. Likewise u is left perpendicular to v and can be denoted by uv.

By definition vu if and only if uv. However, vu need not imply uv.

For example, let V=kk and b((v1,v2),(u1,u2))=v1u2. Then b((0,1),(1,0))=0 so (0,1)(1,0), or equivalently, (1,0)(0,1). However b((1,0),(0,1))=10 so (1,0) is not right perpendicular to (0,1) and (0,1) is not left perpendicular to (1,0).

Title left / right perpendicular
Canonical name LeftRightPerpendicular
Date of creation 2013-03-22 16:13:05
Last modified on 2013-03-22 16:13:05
Owner Algeboy (12884)
Last modified by Algeboy (12884)
Numerical id 7
Author Algeboy (12884)
Entry type Derivation
Classification msc 15A63
Defines left perpendicular
Defines right perpendicular