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MathGroup Archive 1999

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Re: Generalization of Greater to matrices

  • To: mathgroup at smc.vnet.net
  • Subject: [mg20287] Re: Generalization of Greater to matrices
  • From: Jens-Peer Kuska <kuska at informatik.uni-leipzig.de>
  • Date: Tue, 12 Oct 1999 03:39:28 -0400
  • Organization: Universitaet Leipzig
  • References: <7trvlu$bsh@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com

Hi Herman,

at first You need a matrix norm, i.e a positive semidefined function
that map a Matrix onto positive real numbers. One common definition may
be

MatrixNorm[m_?MatrixQ] := Abs[Det[m]]

since a determinat is a expensive operation it is better to calculate
the value
one and to store the results:

MatrixSort[mtab_]:= First /@ Sort[{#, MatrixNorm[#]} & /@ mtab, Last[#1]
> Last[#2] &]

The result is the sorted list of matrices.

Hope that helps
  Jens


Hermann Meier wrote:
> 
> Dear Mathematica Users,
> 
> I tried to solve the following seemingly not to complicated problem, to no
> avail.
> 
> M1, M2, M3 ...  are matrices of equal dimensions. The task is to  find the
> "greatest" among them. The elements of this matrix, say M2,  should be (in
> principle) greater than all the corresponding elements of M1, M3, Mx....
> Furthermore, a kind of a "slack variable" (s) should be introduced.

SNIP SNAPP


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