The Equivalent Standard Forms of a Class of Tropical Matrices and Centralizer Groups - Yanliang Cheng (Mathematics)
In this paper, the equivalent standard forms of tropical idempotent strongly definite matrices are introduced. In particular, the observation of the equivalent standard forms of tropical idempotent normal matrices is given. An equivalence relation <semantics>ρ</semantics> on the set of all tropical idempotent normal matrices, which is relevant to their centralizer groups, is introduced and studied. It is proved that every <semantics>ρ</semantics>-class contains at least one strongly regular tropical idempotent normal matrix. Furthermore, a structural description of the centralizer groups of partial strongly regular tropical idempotent normal matrices is given.