Supertropical matrix algebra III: Powers of matrices and their supertropical eigenvalues

Zur Izhakian; Louis Rowen

doi:10.1016/j.jalgebra.2011.06.002

Supertropical matrix algebra III: Powers of matrices and their supertropical eigenvalues

Zur Izhakian, Louis Rowen

Research output: Contribution to journal › Article › peer-review

18 Scopus citations

Abstract

We investigate powers of supertropical matrices, with special attention to the role of the coefficients of the supertropical characteristic polynomial (especially the supertropical trace) in controlling the rank of a power of a matrix. This leads to a Jordan-type decomposition of supertropical matrices, together with a supertropical eigenspace decomposition of a power of an arbitrary supertropical matrix.

Original language	English
Pages (from-to)	125-149
Number of pages	25
Journal	Journal of Algebra
Volume	341
Issue number	1
DOIs	https://doi.org/10.1016/j.jalgebra.2011.06.002
State	Published - 1 Sep 2011
Externally published	Yes

Keywords

Eigenspaces
Jordan decomposition
Nilpotent and ghostpotent matrices
Powers of matrices
Tropical algebra

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10.1016/j.jalgebra.2011.06.002

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abstract = "We investigate powers of supertropical matrices, with special attention to the role of the coefficients of the supertropical characteristic polynomial (especially the supertropical trace) in controlling the rank of a power of a matrix. This leads to a Jordan-type decomposition of supertropical matrices, together with a supertropical eigenspace decomposition of a power of an arbitrary supertropical matrix.",

keywords = "Eigenspaces, Jordan decomposition, Nilpotent and ghostpotent matrices, Powers of matrices, Tropical algebra",

author = "Zur Izhakian and Louis Rowen",

note = "Funding Information: ✩ This research is supported by the Israel Science Foundation (grant No. 448/09). * Corresponding author. E-mail addresses: [email protected] (Z. Izhakian), [email protected] (L. Rowen). 1 The first author has been a Leibniz Fellow in the Oberwolfach Leibniz Fellows Forschungsinstitut Oberwolfach, Germany.",

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N1 - Funding Information: ✩ This research is supported by the Israel Science Foundation (grant No. 448/09). * Corresponding author. E-mail addresses: [email protected] (Z. Izhakian), [email protected] (L. Rowen). 1 The first author has been a Leibniz Fellow in the Oberwolfach Leibniz Fellows Forschungsinstitut Oberwolfach, Germany.

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KW - Eigenspaces

KW - Jordan decomposition

KW - Nilpotent and ghostpotent matrices

KW - Powers of matrices

KW - Tropical algebra

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Supertropical matrix algebra III: Powers of matrices and their supertropical eigenvalues

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