# hyperplane

Let $E$ be a linear space over a field $k$. A hyperplane $H$ in $E$ is defined as the set of the form

 $H=\{x\in E:f(x)=a\}$

where $a\in k$ and $f$ is a nonzero linear functional, $f\colon E\to k$. If $k=\mathbb{R}$ or $\mathbb{C}$, then $H$ is called a real hyperplane or complex hyperplane respectively.

Remark. When $k=\mathbb{C}$, 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 Hyperplane 2013-03-22 15:15:12 2013-03-22 15:15:12 georgiosl (7242) georgiosl (7242) 9 georgiosl (7242) Definition msc 46H05 real hyperplane complex hyperplane