TY - JOUR

T1 - Supertropical matrix algebra II

T2 - Solving tropical equations

AU - Izhakian, Zur

AU - Rowen, Louis

N1 - 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

PY - 2011/11

Y1 - 2011/11

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=80155171896&partnerID=8YFLogxK

U2 - 10.1007/s11856-011-0133-2

DO - 10.1007/s11856-011-0133-2

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AN - SCOPUS:80155171896

SN - 0021-2172

VL - 186

SP - 69

EP - 96

JO - Israel Journal of Mathematics

JF - Israel Journal of Mathematics

IS - 1

ER -