       • To: mathgroup at smc.vnet.net
• Subject: [mg25227] RowReduce of badly conditioned matrix
• From: Camillo Ressl <car at ipf.tuwien.ac.at>
• Date: Fri, 15 Sep 2000 02:21:58 -0400 (EDT)
• Organization: Vienna University of Technology, Austria
• Sender: owner-wri-mathgroup at wolfram.com

```Hallo!

I have the following problem: I have a matrix a with 24 rows and 42
colums.Its elements are given in double precision. For this matrix the
following holds:

Rank[a]  == Rank[a.Transpose[a]]  = 21

In:=  {u,md,v}= SingularValues[a];

In:= md

Out= {1.41421, 1.41421, 1.41421, 1.13491, 1.13488, 1.00081,
1.00002,

>    1.00001, 1.00001, 1.00001, 1., 1., 1., 0.999999, 0.999987,
0.999987,

>    0.999986, 0.999978, 0.998748, 0.844348, 0.843791}

And now I want to compute the rowreduced matrix of a and I get the
following error message.

In:= RowReduce[a]

RowReduce::luc:
Result for RowReduce of badly conditioned matrix {<<24>>}
may contain significant numerical errors.

7
Out= {{1, 0, 0, 0, 0, 0, 0, 0, 4.78983 10 , 0, 0, 0, 0, 0, 0, 0,
...etc.

I have no idea what the reason for this message could be since the
Singular Values seem o.k.
And the rank-defect of 3 should not be the reason since I expect 3
zero-rows for the rowreduced matrix.

Is there someone who can help me or give me at least a few hints?

Many thanks for any help.

Camillo

```

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