RowReduce of badly conditioned matrix

*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[298]:= {u,md,v}= SingularValues[a]; In[299]:= md Out[299]= {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[300]:= RowReduce[a] RowReduce::luc: Result for RowReduce of badly conditioned matrix {<<24>>} may contain significant numerical errors. 7 Out[300]= {{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

**Follow-Ups**:**Re: RowReduce of badly conditioned matrix***From:*Daniel Lichtblau <danl@wolfram.com>