MathOverflow is a question and answer site for professional mathematicians. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

Consider the collection of $n$ by $n$ matrices $$S=\{ A: A_{ij}\le0,\quad (-1)^{c_i}\det A(P_i;Q_i)<0 \quad \text{for} \quad i=1,\ldots, k\}$$ where $c_i\in \{0,1\}$, $P_i$ and $Q_i$ are disjoint index sets, and $A(P_i;Q_i)$ is the submatrix formed by taking just the rows $P_i$ and columns $Q_i$ of $A$.

What kind of conditions on $S$ would be natural to add to guarantee that $S$ is path connected? Also what areas of mathematics are useful in trying to answer these types of path connected questions?

share|cite|improve this question
    
Set of non-positive matrices in general position. I would look at realisable oriented matroids. The chapter in booktopia.com.au/oriented-matroids-gunter-m-ziegler/… addresses these things – Rabee Tourky Jun 21 at 4:54

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Browse other questions tagged or ask your own question.