Mathematics-Online lexicon: Simplex

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	Mathematics-Online lexicon:
	Simplex

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A simplex $S\subset\mathbb{R}^n$ is the convex hull of

points

which are not contained in a hyperplane of $\mathbb{R}^n .$

$\displaystyle S = \{ x =\sum_{j}\alpha_j p_j\,,\, \sum_{j}\alpha_j\le 1,\ \alpha_j\ge 0 \}$

$\includegraphics[width=5cm]{a_simplex1}$		$\includegraphics[width=6cm]{a_simplex2}$
n=2		n=3

A simplex in $\mathbb{R}^2$ is a triangle and in $\mathbb{R}^3$ a simplex is a tetrahedron.

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see also:

automatically generated 8/ 4/2008