Abstract
We investigate powers of supertropical matrices, with special attention to the role of the coefficients of the supertropical characteristic polynomial (especially the supertropical trace) in controlling the rank of a power of a matrix. This leads to a Jordan-type decomposition of supertropical matrices, together with a supertropical eigenspace decomposition of a power of an arbitrary supertropical matrix.
| Original language | English |
|---|---|
| Pages (from-to) | 125-149 |
| Number of pages | 25 |
| Journal | Journal of Algebra |
| Volume | 341 |
| Issue number | 1 |
| DOIs | |
| State | Published - 1 Sep 2011 |
Bibliographical note
Funding Information:✩ This research is supported by the Israel Science Foundation (grant No. 448/09). * Corresponding author. E-mail addresses: [email protected] (Z. Izhakian), [email protected] (L. Rowen). 1 The first author has been a Leibniz Fellow in the Oberwolfach Leibniz Fellows Forschungsinstitut Oberwolfach, Germany.
Funding
✩ This research is supported by the Israel Science Foundation (grant No. 448/09). * Corresponding author. E-mail addresses: [email protected] (Z. Izhakian), [email protected] (L. Rowen). 1 The first author has been a Leibniz Fellow in the Oberwolfach Leibniz Fellows Forschungsinstitut Oberwolfach, Germany.
| Funders | Funder number |
|---|---|
| Israel Science Foundation | 448/09 |
Keywords
- Eigenspaces
- Jordan decomposition
- Nilpotent and ghostpotent matrices
- Powers of matrices
- Tropical algebra