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MathGroup Archive 2007

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Re: MatrixRank Modulus->8 - BUG

  • To: mathgroup at smc.vnet.net
  • Subject: [mg73680] Re: [mg73636] MatrixRank Modulus->8 - BUG
  • From: Daniel Lichtblau <danl at wolfram.com>
  • Date: Sat, 24 Feb 2007 02:23:05 -0500 (EST)
  • References: <200702230943.EAA17928@smc.vnet.net>

janos wrote:
> Let us introduce
> U = {{4, 1, 5}, {3, 4, 2}, {7, 2, 4}};
> V = {{5, 1, 4}, {2, 4, 3}, {4, 2, 7}};
> and calculate the ranks:
> {MatrixRank[U, Modulus -> 8], MatrixRank[V, Modulus -> 8]}
> {2,3}
> Version:
> 5.2 for Microsoft Windows
> 
> I do not think the rank should depend on the order of columns.
> Any idea?
> 
> Thanks,
> 
> Janos


Might be a smallish bug. I think maybe it should return unevaluated. 
Since we're not working over a field I don't know that the rank is well 
defined.

If it is, my guess is it would depend on the dimension of the null 
space. That can be assessed correctly using the Hermite decomposition on 
the augmented matrix

U2 = Join[U,8*IdentityMatrix[Length[U]]]

A correct interpretation of the result would indicate there are no null 
vectors, hence rank would be 3. But again, offhand I'm not sure this is 
really a correct definition.


Daniel Lichtblau
Wolfram Research


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