Dependence of supertropical eigenspaces. (English) Zbl 1378.15006

This paper is devoted to the analysis of the issues that causes tropical eigenspaces of distinct supertropical eigenvalues of a nonsingular matrix A to be dependent. Starting with a long survey of the recent results of tropical polynomials, the authors introduce properties of matrices and vectors in the tropical structure, with definitions extended to the supertropical framework. Next, they analyze the dependence between eigenvectors, using their definition according to the so-called eigenvectors algorithm described by Z. Izhakian and L. Rowen [Isr. J. Math. 186, 69–96 (2011; Zbl 1277.15013)]. Some special cases are resolved. In the end, sufficient conditions for independence are stated, and two conjectures on the eigenvectors of the quasi-inverse of a matrix are proposed.


15A18 Eigenvalues, singular values, and eigenvectors
15A09 Theory of matrix inversion and generalized inverses
15A15 Determinants, permanents, traces, other special matrix functions
15A80 Max-plus and related algebras
15B33 Matrices over special rings (quaternions, finite fields, etc.)


Zbl 1277.15013
Full Text: DOI arXiv


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