Efficient Recognition of Totally Nonnegative Matrix Cells

@article{Launois2014EfficientRO,
  title={Efficient Recognition of Totally Nonnegative Matrix Cells},
  author={St{\'e}phane Launois and T. Lenagan},
  journal={Foundations of Computational Mathematics},
  year={2014},
  volume={14},
  pages={371-387}
}
The space of m × 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 Peña 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… CONTINUE READING