Let E be a linear spacePlanetmathPlanetmath over a field k. A hyperplanePlanetmathPlanetmath H in E is defined as the set of the form


where ak and f is a nonzero linear functionalPlanetmathPlanetmath, f:Ek. If k= or , then H is called a real hyperplane or complex hyperplane respectively.

Remark. When k=, the word “hyperplane” also has a more restrictive meaning: it is the zero set of a complex linear functional (by setting a=0 above).

Title hyperplane
Canonical name Hyperplane
Date of creation 2013-03-22 15:15:12
Last modified on 2013-03-22 15:15:12
Owner georgiosl (7242)
Last modified by georgiosl (7242)
Numerical id 9
Author georgiosl (7242)
Entry type Definition
Classification msc 46H05
Defines real hyperplane
Defines complex hyperplane