
<A NAME=svd>

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



<B>SVD</B> _ _ _  _ _ _  _ _ _  _ _ _ <B>operator</B><P>
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Singular value decomposition: 
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syntax: </H3>
<em>svd</em>(&lt;matrix&gt;) 
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&lt;matrix&gt; :- a 
<A HREF=r37_0345.html>matrix</A> containing only numeric entries. 
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<em>svd</em>computes the singular value decomposition of &lt;matrix&gt;. 
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It returns 
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{U,P,V} 
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where A = U*P*V^T 
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and P = diag(sigma(1) ... sigma(n)). 
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sigma(i) for i= 1 ... n are the singular values of 
&lt;matrix&gt;. 
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n is the column dimension of &lt;matrix&gt;. 
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The singular values of &lt;matrix&gt; are the non-negative square roots 
of the eigenvalues of A^T*A. 
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U and V are such that U*U^T = V*V^T = V^T*V = Id. 
Id is the identity matrix. 
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examples: </H3>
<P><PRE><TT>

Q := mat((1,3),(-4,3)); 

       [1   3]
  q := [     ]
       [-4  3]



on rounded; 

svd(Q); 

  {
   [ 0.289784137735    0.957092029805]
   [                                 ]
   [ - 0.957092029805  0.289784137735]
   ,
   [5.1491628629       0      ]
   [                          ]
   [     0        2.9130948854]
   ,
   [ - 0.687215403194   0.726453707825  ]
   [                                    ]
   [ - 0.726453707825   - 0.687215403194]
  }

</TT></PRE><P>