hyperplane
Let be a linear space over a field . A hyperplane in is defined as the set of the form
where and is a nonzero linear functional, . If or , then is called a real hyperplane or complex hyperplane respectively.
Remark. When , the word “hyperplane” also has a more restrictive meaning: it is the zero set of a complex linear functional (by setting above).
Title | hyperplane |
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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 |