关于矩阵幂的秩不变的充要条件的一个证明

A Necessary and Sufficient Condition for Invariant Rank of Powers of Matrix

设P为一般数域,A=(aij)n×n为P上的矩阵,R(A)为A的秩,利用矩阵的有理标准形给出了A满足R(A^(2))=R(A)的充分必要条件的一个新的证明.

Let P be a number field, A=(aij)n×nbe a matrix over P,R(A)be the rank of A.We present a new proof of a necessary and sufficient condition for A satisfying R(A^(2))=R(A) by the rational canonical form of matrix.