Abstract
Continuing 4, this article investigates finer points of supertropical vector spaces, including dual bases and bilinear forms, with supertropical versions of standard classical results such as the Gram-Schmidt theorem and Cauchy-Schwartz inequality, and change of base. We also present the supertropical version of quadratic forms, and see how they correspond to symmetric supertropical bilinear forms.
| Original language | English |
|---|---|
| Pages (from-to) | 865-883 |
| Number of pages | 19 |
| Journal | Linear and Multilinear Algebra |
| Volume | 60 |
| Issue number | 7 |
| DOIs | |
| State | Published - Jul 2012 |
Bibliographical note
Funding Information:The work of the first and third authors has been supported by the Israel Science Foundation, grant 448/09. The second author was supported in part by the Gelbart Institute at Bar-Ilan University, the Minerva Foundation at Tel-Aviv University, the Mathematics Department of Bar-Ilan University, and the Emmy Noether Institute.
Funding
The work of the first and third authors has been supported by the Israel Science Foundation, grant 448/09. The second author was supported in part by the Gelbart Institute at Bar-Ilan University, the Minerva Foundation at Tel-Aviv University, the Mathematics Department of Bar-Ilan University, and the Emmy Noether Institute.
| Funders | Funder number |
|---|---|
| Emmy Noether Research Institute for Mathematics | |
| Gelbart Institute at Bar-Ilan University | |
| Department of Mathematics, Bar-Ilan University | |
| Israel Science Foundation | 448/09 |
| Tel Aviv University |
Keywords
- bilinear form
- change of base semirings
- d-base
- dual base
- linear algebra
- s-base
- tropical algebra
- vector space