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

Supertropical matrix algebra III: Powers of matrices and generalized eigenspaces