Efficient Recognition of Totally Nonnegative Matrix Cells |
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| Authors: | S Launois T Lenagan |
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| Institution: | 1. School of Mathematics, Statistics & Actuarial Science, University of Kent, Canterbury, Kent, CT2 7NF, UK
2. Maxwell Institute for Mathematical Sciences, School of Mathematics, University of Edinburgh, James Clerk Maxwell Building, King’s Buildings, Mayfield Road, Edinburgh, EH9 3JZ, Scotland, UK
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| Abstract: | 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 membership which only involves mp minors, thus extending the Gasca and Peña result to all totally nonnegative cells. |
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