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| − | A variety is a mathematical construct used to define [[Decision Surfaces_OldKiwi]]. Intuitively, it is the zero set of polynomials that tells 'what kind of set can you get?' in a particular case. | + | A variety is a mathematical construct used to define [[Decision Surfaces_OldKiwi|Decision Surfaces]]. Intuitively, it is the zero set of polynomials that tells 'what kind of set can you get?' in a particular case. |
Definition: | Definition: | ||
Latest revision as of 09:46, 10 June 2013
Varieties
from Lecture 1, ECE662, Spring 2010
A variety is a mathematical construct used to define Decision Surfaces. Intuitively, it is the zero set of polynomials that tells 'what kind of set can you get?' in a particular case.
Definition: Let
$ \mathbf{x}\in {\Re}^n $ and $ \mathbf{P} $ be set of polynomials: $ \Re ^n \rightarrow \Re $.
Then variety is given by
$ \mathbf{V} (\mathbf{P})=\left\{ \mathbf{x}\in \Re ^n : p(\mathbf{x})=0 \ for \ all \ p \in \mathbf{P} \right\} $
