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?



Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Browse other questions tagged or ask your own question.