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<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 3.2 Final//EN">
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<TITLE>RANK Calculate the Rank of a Matrix
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<H2>RANK Calculate the Rank of a Matrix
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<P>
Section: <A HREF=sec_array.html> Array Generation and Manipulations </A>
<H3>Usage</H3>
Returns the rank of a matrix. There are two ways to use
the <code>rank</code> function is
<PRE>
y = rank(A,tol)
</PRE>
<P>
where <code>tol</code> is the tolerance to use when computing the
rank. The second form is
<PRE>
y = rank(A)
</PRE>
<P>
in which case the tolerance <code>tol</code> is chosen as
<PRE>
tol = max(size(A))*max(s)*eps,
</PRE>
<P>
where <code>s</code> is the vector of singular values of <code>A</code>. The
rank is computed using the singular value decomposition <code>svd</code>.
<H3>Examples</H3>
Some examples of matrix rank calculations
<PRE>
--> rank([1,3,2;4,5,6])
ans =
2
--> rank([1,2,3;2,4,6])
ans =
1
</PRE>
<P>
Here we construct an ill-conditioned matrix, and show the use
of the <code>tol</code> argument.
<PRE>
--> A = [1,0;0,eps/2]
A =
1.0000 0
0 0.0000
--> rank(A)
ans =
1
--> rank(A,eps/8)
ans =
2
</PRE>
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