
<A NAME=NULLSPACE>

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



<B>NULLSPACE</B> _ _ _  _ _ _  _ _ _  _ _ _ <B>operator</B><P>
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syntax: </H3>
<em>nullspace</em>(&lt;matrix\_expression&gt;) 
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&lt;nullspace&gt; calculates for its 
<A HREF=r37_0345.html>matrix</A> argument, 
<em>a</em>, a list of 
linear independent vectors (a basis) whose linear combinations satisfy the 
equation a x = 0. The basis is provided in a form such that as many 
upper components as possible are isolated. 
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 <P> <H3> 
examples: </H3>
<P><PRE><TT>
nullspace mat((1,2,3,4),(5,6,7,8)); 


         {
           [ 1  ]
           [    ]
           [ 0  ]
           [    ]
           [ - 3]
           [    ]
           [ 2  ]
           ,
           [ 0  ]
           [    ]
           [ 1  ]
           [    ]
           [ - 2]
           [    ]
           [ 1  ]
          }

</TT></PRE><P>Note that with <em>b := nullspace a</em>, the expression <em>lengt
h b</em> is 
the nullity/ of A, and that <em>second length a - length b</em> 
calculates the rank/ of A. The rank of a matrix expression can 
also be found more directly by the 
<A HREF=r37_0347.html>rank</A> operator. 
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In addition to the REDUCE matrix form, <em>nullspace</em> accepts as input a 
matrix given as a 
<A HREF=r37_0053.html>list</A> of lists, that is interpreted as a row matrix. If
 
that form of input is chosen, the vectors in the result will be 
represented by lists as well. This additional input syntax facilitates 
the use of <em>nullspace</em> in applications different from classical linear 
algebra. 
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