File r37/lisp/csl/html/r37_0606.html artifact 2ffd9236aa part of check-in b7c3de82ef

<A NAME=pseudo_inverse>

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



<B>PSEUDO_INVERSE</B> _ _ _  _ _ _  _ _ _  _ _ _ <B>operator</B><P>
<P>
 
<P>
<P>
 <P> <H3> 
syntax: </H3>
<em>pseudo_inverse</em>(&lt;matrix&gt;) 
<P>
<P>
<P>
&lt;matrix&gt; :- a 
<A HREF=r37_0345.html>matrix</A>. 
<P>
<P>
<em>pseudo_inverse</em>, also known as the Moore-Penrose inverse, 
computes the pseudo inverse of &lt;matrix&gt;. 
<P>
<P>
Given the singular value decomposition of &lt;matrix&gt;, i.e: 
A = U*P*V^T, then the pseudo inverse A^-1 is defined by 
A^-1 = V^T*P^-1*U. 
<P>
<P>
Thus &lt;matrix&gt; * pseudo_inverse(A) = Id. 
(Id is the identity matrix). 
<P>
<P>
 <P> <H3> 
examples: </H3>
<P><PRE><TT>

R := mat((1,2,3,4),(9,8,7,6)); 

       [1  2  3  4]
  r := [          ]
       [9  8  7  6]



on rounded; 

pseudo_inverse(R); 

  [ - 0.199999999996      0.100000000013   ]
  [                                        ]
  [ - 0.0499999999988    0.0500000000037   ]
  [                                        ]
  [ 0.0999999999982     - 5.57825497203e-12]
  [                                        ]
  [  0.249999999995      - 0.0500000000148 ]

</TT></PRE><P>Related functions: 
<A HREF=r37_0616.html>svd</A>. 
<P>
<P>