Some notes on adjoint matrices over commutative integral domain

摘要

Using the rational canonical form of A, we present the rational canonical form of the adjoint matrices A*. Moreover, it is proved that the adjoint matrix of an idempotent (nilpotent, unipotent) matrix is also idempotent (nilpotent, unipotent) over a commutative integral domain. (C) 2003 Elsevier Inc. All rights reserved.