2009/02/12 by Zur Izhakian, Izhakian, Zur, Louis Rowen +1
Computer Science · Mathematics · #15A03 #15A09 #15A15 #16Y60 #65F15 #Advanced Topics in Algebra #Combinatorics (math.CO) #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics #Polynomial and algebraic computation #math.AC #math.CO #msc:15A03 #msc:15A09 #msc:15A15 #msc:16Y60 #msc:65F15
paper · pdf · doi:10.48550/arxiv.0902.2159
16 pages
openalex publication_date 2009/02/12 · arxiv created 2009/12/07 · arxiv updated 2009/12/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.