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<A NAME=gram_schmidt>

<TITLE>gram_schmidt</TITLE></A>
<b><a href=r37_idx.html>INDEX</a></b><p><p>



<B>GRAM_SCHMIDT</B> _ _ _  _ _ _  _ _ _  _ _ _ <B>operator</B><P>
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 <P> <H3> 
syntax: </H3>
<em>gram_schmidt</em>({&lt;vec\_list&gt;}) 
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(If you are feeling lazy then the braces can be omitted.) 
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&lt;vec\_list&gt; :- linearly independent vectors. Each vector must be 
written as a list, eg:{1,0,0}. 
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<em>gram_schmidt</em>performs the gram_schmidt orthonormalization on 
the input vectors. 
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It returns a list of orthogonal normalized vectors. 
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 <P> <H3> 
examples: </H3>
<P><PRE><TT>

gram_schmidt({{1,0,0},{1,1,0},{1,1,1}}); 


  {{1,0,0},{0,1,0},{0,0,1}} 



gram_schmidt({{1,2},{3,4}}); 


        1         2        2*sqrt(5)   -sqrt(5)
  {{ ------- , ------- },{ --------- , -------- }}
     sqrt(5)   sqrt(5)         5          5

</TT></PRE><P>