Supertropical matrix algebra III: Powers of matrices and generalized eigenspaces

Abstract

We investigate powers of supertropical matrices, with special attention to the role of the co- e±cients 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 generalized eigenspace decomposition of a power of an arbitrary supertropical matrix.