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| + | from [[Lecture_1_-_Introduction_OldKiwi|Lecture 1, ECE662, Spring 2010]] | ||
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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]]. Intuitively, it is the zero set of polynomials that tells 'what kind of set can you get?' in a particular case. | ||
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<math>\mathbf{V} (\mathbf{P})=\left\{ \mathbf{x}\in \Re ^n : p(\mathbf{x})=0 \ for \ all \ p \in \mathbf{P} \right\}</math> | <math>\mathbf{V} (\mathbf{P})=\left\{ \mathbf{x}\in \Re ^n : p(\mathbf{x})=0 \ for \ all \ p \in \mathbf{P} \right\}</math> | ||
| + | ---- | ||
| + | [[Lecture_1_-_Introduction_OldKiwi|Back to Lecture 1, ECE662, Spring 2010]] | ||
Revision as of 10:45, 10 June 2013
Varieties
from Lecture 1, ECE662, Spring 2010
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.
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\} $
