Supertropical matrix algebra II: Solving tropical equations

Zur Izhakian, Louis Rowen

Research output: Contribution to journalArticlepeer-review

27 Scopus citations

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 × n matrix has n distinct supertropical eigenvalues but their supertropical eigenvectors are tropically dependent.

Original languageEnglish
Pages (from-to)69-96
Number of pages28
JournalIsrael Journal of Mathematics
Volume186
Issue number1
DOIs
StatePublished - Nov 2011

Bibliographical note

Funding Information:
∗The first author was supported by the Chateaubriand scientific post-doctorate fellowship, Ministry of Science, French Government, 2007-2008. This research is supported in part by the Israel Science Foundation, grant No. 448/09. Received August 4, 2009 and in revised form January 27, 2010

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