Abstract
The space of m x p totally nonnegative real matrices has a stratification into totally
nonnegative cells. The largest such cell is the space of totally positive matrices. There is a well-known criterion due to Gasca and Pena for testing a real matrix for total positivity. This criterion involves testing mp minors. In contrast, there is no known small set of minors for testing for total nonnegativity. In this paper, we show that for each of the totally nonnegative cells there is a test for membership which only involves mp minors, thus extending the Gasca and Pena result to all totally nonnegative cells.
nonnegative cells. The largest such cell is the space of totally positive matrices. There is a well-known criterion due to Gasca and Pena for testing a real matrix for total positivity. This criterion involves testing mp minors. In contrast, there is no known small set of minors for testing for total nonnegativity. In this paper, we show that for each of the totally nonnegative cells there is a test for membership which only involves mp minors, thus extending the Gasca and Pena result to all totally nonnegative cells.
| Original language | English |
|---|---|
| Number of pages | 21 |
| Journal | Foundations of Computational Mathematics |
| Early online date | 17 Sept 2013 |
| DOIs | |
| Publication status | Published - 2013 |
Keywords / Materials (for Non-textual outputs)
- Totally nonnegative cells