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arXiv · 0902.2159

Supertropical Matrix Algebra II: Solving tropical equations

Zur Izhakian·Louis Rowen
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Abstract

We continue the study of matrices over a supertropical algebra, proving the existence of a tangible adjoint of $A$, which provides the unique right (resp. left) quasi-inverse maximal with respect to the right (resp. left) quasi-identity matrix corresponding to $A$; this provides a unique maximal (tangible) solution to supertropical vector equations, via a version of Cramer's rule. We also describe various properties of this tangible adjoint, and use it to compute supertropical eigenvectors, thereby producing an example in which an $n\times n$ matrix has $n$ distinct supertropical eigenvalues but their supertropical eigenvectors are tropically dependent.

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Zur Izhakian, Louis Rowen. 2009-02-12. Supertropical Matrix Algebra II: Solving tropical equations. https://arxiv.org/abs/0902.2159

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