Abstract
We study the combinatorial description of the LDU-decomposition of totally positive matrices. We give a description of the lower triangular L, the diagonal D, and the upper triangular U matrices of the LDU-decomposition of totally positive matrices in terms of the combinatorial structure of essential planar networks described by Fomin and Zelevinsky [5]. Similarly, we find a combinatorial description of the inverses of these matrices. In addition, we provide recursive formulae for computing the L, D, and U matrices of a totally positive matrix.
| Original language | English |
|---|---|
| Pages (from-to) | 51-71 |
| Number of pages | 21 |
| Journal | Glasnik Matematicki |
| Volume | 53 |
| Issue number | 1 |
| DOIs | |
| Publication status | Published - 2018 |
Keywords
- LDU factorization
- Planar networks
- Totally positive matrices