The Minimum Rank Problem: a counterexample

Details The Minimum Rank Problem: a counterexample The Minimum Rank Problem: a counterexample

2007-08-13

arxiv.org/abs/0708.1707v2

Mathematics

Combinatorics

4 pages, 1 figure

Scientific paper

We provide a counterexample to a recent conjecture that the minimum rank of every sign pattern matrix can be realized by a rational matrix. We use one of the equivalences of the conjecture and some results from projective geometry. As a consequence of the counterexample, we show that there is a graph for which the minimum rank over the reals is strictly smaller than the minimum rank over the rationals. We also make some comments on the minimum rank of sign pattern matrices over different subfields of $\mathbb R$.

Affiliated with

Also associated with

No associations

Rating

The Minimum Rank Problem: a counterexample does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with The Minimum Rank Problem: a counterexample, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and The Minimum Rank Problem: a counterexample will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-23549