Supertropical linear algebra
Abstract
The objective of this paper is to lay out the algebraic theory of supertropical vector spaces and linear algebra, utilizing the key antisymmetric relation of ``ghost surpasses.''Special attention is paid to the various notions of ``base,'' which include d-base and s-base, and these are compared to other treatments in the tropical theory. Whereas the number of elements in a d-base may vary according to the d-base, it is shown that when an s-base exists, it is unique up to permutation and multiplication by scalars, and can be identified with a set of ``critical'' elements. Linear functionals and the dual space are also studied, leading to supertropical bilinear forms and a supertropical version of the Gram matrix, including its connection to linear dependence, as well as a supertropical version of a theorem of Artin.
Cite
@article{arxiv.1008.0025,
title = {Supertropical linear algebra},
author = {Zur Izhakian and Manfred Knebusch and Louis Rowen},
journal= {arXiv preprint arXiv:1008.0025},
year = {2010}
}
Comments
28 pages