Mathematics-Online lexicon: Gram-Schmidt Method

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	Mathematics-Online lexicon:
	Gram-Schmidt Method

A B C D E F G H I J K L M N O P Q R S T U V W X Y Z

Starting from a given basis $b_1,\ldots,b_n$ we can construct an orthonormal basis $u_1,\ldots,u_n$ as follows: We successively define

$\displaystyle \tilde u_j$	$\displaystyle =$	$\displaystyle b_j - \sum_{k<j} \langle b_j,u_k \rangle u_k,$
$\displaystyle u_j$	$\displaystyle =$	$\displaystyle \tilde u_j / \Vert\tilde u_j\Vert$

for $k=1,\ldots,n$ .

(Authors: App/Burkhardt/Höllig)

Example:

automatically generated 3/21/2005