Supertropical linear algebra

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 identi¯ed 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.

Keywords

Tropical algebra, semimodules and supertropical vector spaces, linear algebra, change of base semirings, linear and bilinear forms, Gram matrix

URI

https://doi.org/10.34657/3281
https://oa.tib.eu/renate/handle/123456789/1725

Citation

Izhakian, Z., Knebusch, M., & Rowen, L. (2010). Supertropical linear algebra (Vol. 2010-14). Oberwolfach : Mathematisches Forschungsinstitut Oberwolfach. https://doi.org//10.14760/OWP-2010-14

Collections

Mathematik
Oberwolfach Preprints (OWP)

License

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