Talk:Unimodular matrix

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Examples of totally unimodular matrices?

Charles Matthews 10:14, 13 Apr 2004 (UTC)

The definition of unimodular matrix is really with +1 or -1, and so I have deleted the special linear group link.

Simon Lacoste-Julien 01:02, 25 Apr 2004 (PST)

[edit] kronecker

Does anybody know if the Kronecker product of two totally unimodular matrices is again totally unimodular?

[edit] integer matrices

I strongly think that you need an additional restriction of unimodular matrices being integer matrices.

Some sources ("Loop Parallelization", Utpal Banerjee) require the inverted matrix to be an integer matrix, even though I think this is unecessary.

--M1ck1 12:10, 1 December 2006 (UTC)

Ok, I also found 2 standard books on the subject that also agree on requiring integer matrices:

  • "Integer and Combinational Optimization", Geroge L. Nemhauser, Laurence A. Wolsey, 1988, page 189
  • "Theory of Linear and Integer Programming", Alexander Schrijver, 1989, page 49

--M1ck1 14:52, 1 December 2006 (UTC)

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