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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\} $


Back to Lecture 1, ECE662, Spring 2010

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