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

**References**:**MatrixRank Modulus->8 - BUG***From:*"janos" <janostothmeister@gmail.com>