The Polynomial Denotation for the Matrix Being Changeable with a Given Matrix
Qingxin Zhang · College Mathematics · 2012
[1] obtained: if there is not the Jordan block corresponding to the scalar matrix in the Jordan canonical form of the matrix A,then the necessary and sufficient condition of AB=BA is that B can be n-1-order polynomial about A.In the paper,we pointed the conclusion is wrong.On the basis of the previously related literatures,we derive ten equivalent characterizations that the matrix B being changeable with given matrix A is the polynomial about A.