most recent 30 from http://mathoverflow.net 2013-05-25T08:40:00Z http://mathoverflow.net/feeds/question/84505 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/84505/path-connected-set-of-matrices unknown (google) 2011-12-29T11:37:57Z 2011-12-30T05:45:29Z

<p>Consider the collection of $n$ by $n$ matrices $$S=\{ A: A_{ij}\le0,\quad (-1)^{c_i}\det A(P_i;Q_i)&lt;0 \quad \text{for} \quad i=1,\ldots, k\}$$ 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 $A$.</p> <p>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?</p>