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

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.