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arXiv · 1008.0025

Supertropical linear algebra

Zur Izhakian·Manfred Knebusch·Louis Rowen
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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.

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Zur Izhakian, Manfred Knebusch, Louis Rowen. 2010-07-30. Supertropical linear algebra. https://arxiv.org/abs/1008.0025

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