Abstract
Extending earlier work on supertropical adjoints and applying symmetrization, we provide a symmetric supertropical version (Formula presented.) of the special linear group (Formula presented.), which we partially decompose into submonoids, based on ‘quasi-identity’ matrices, and we display maximal sub-semigroups of (Formula presented.). We also study the monoid generated by (Formula presented.) and its natural submonoids. Several illustrative examples are given of unexpected behavior. We describe the action of elementary matrices on (Formula presented.), which enables one to connect different matrices in (Formula presented.), but in a weaker sense than the classical situation.
| Original language | English |
|---|---|
| Pages (from-to) | 1461-1483 |
| Number of pages | 23 |
| Journal | Linear and Multilinear Algebra |
| Volume | 66 |
| Issue number | 7 |
| Early online date | 16 Aug 2017 |
| DOIs | |
| Publication status | Published - 2018 |
Keywords
- elementary matrix
- matrix monoid
- quasi-identity
- special linear monoid
- Supertropical matrix algebra
- tropical adjoint matrix