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Supertropical matrix algebra. III: Powers of matrices and their supertropical eigenvalues. (English) Zbl 1283.15055

Summary: 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.
For Parts I and II, see [Isr. J. Math. 182, 383–424 (2011; Zbl 1215.15018); ibid. 186, 69–96 (2011; Zbl 1277.15013)].

MSC:

15A30 Algebraic systems of matrices
15A15 Determinants, permanents, traces, other special matrix functions
15A80 Max-plus and related algebras
16S50 Endomorphism rings; matrix rings
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References:

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