File r37/lisp/csl/html/r37_0591.html artifact 315e60ac36 part of check-in 8e196c7117

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