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MatrixRank[m, Modulus -> 5] is broken

• To: mathgroup at smc.vnet.net
• Subject: [mg97055] MatrixRank[m, Modulus -> 5] is broken
• From: ilan <ilanorv at cs.bgu.ac.il>
• Date: Wed, 4 Mar 2009 07:11:23 -0500 (EST)

I have a strange problem.
I ask for MatrixRank of matrix over the reals without Modulus and I get some number, assume 5;

next I add a raw into this matrix and ask for the rank and I get 5;

next I do both calculations using Modulus -> 7 and get 4 and 5.

There is a problem!!! 
if a the additional raw was linear depended over the reals, it m-u-s-t be linear depended over Modulus because a linear combination for this extra row using other rows is valid when we apply Modulus -> 7.
Therefor I suppose to get 4 and 4.

what is the conclusion?

• Follow-Ups:
  • Re: MatrixRank[m, Modulus -> 5] is broken
    • From: Daniel Lichtblau <danl@wolfram.com>