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Mathematics-Online course: Linear Algebra - Basic Structures - Bases

Gram-Schmidt Method

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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)

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  automatically generated 4/21/2005