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 language | English |
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Pages (from-to) | 69-96 |
Number of pages | 28 |
Journal | Israel Journal of Mathematics |
Volume | 186 |
Issue number | 1 |
DOIs | |
State | Published - 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
Funding
∗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
Funders | Funder number |
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Ministry of Science, French Government | |
Israel Science Foundation | 448/09 |