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Strange behavior of MatrixConditionNumber

• To: mathgroup at smc.vnet.net
• Subject: [mg66541] Strange behavior of MatrixConditionNumber
• From: The Phantom <phantom at aol.com>
• Date: Fri, 19 May 2006 03:40:12 -0400 (EDT)
• Sender: owner-wri-mathgroup at wolfram.com

I get the following in Mathematica 5.2:

<<LinearAlgebra`MatrixManipulation`

     ( 5 -8 -9 -7 -4 )
     ( 5  5 -8  3  1 )
 a = ( 3 -2 -6  8 -1 );
     ( 1 -7  9 -5 -2 )
     (-9  9 -4 -7 -5 )

 q = SetPrecision[a,99];

  N[MatrixConditionNumber[q,2],12]
Out(1) = 6.50915201983

  N[Norm[q,2]*Norm[Inverse[q],2],12]
Out(2) = 7.54449348901

These two values should be the same, shouldn't they?

And what's really strange, I get different values for
N[MatrixConditionNumber[q,2],12] when I execute the program repeatedly.

Does anybody get this strange result?

• Follow-Ups:
  • Re: Strange behavior of MatrixConditionNumber
    • From: Daniel Lichtblau <danl@wolfram.com>