实对称矩阵的一个新刻画

A New Characterization of Real Symmetric Matrix

设A为实矩阵,则A为对称矩阵的充分必要条件是AA^(T)=A^(T)A=A^(2).本文主要对此结果做了推广,得到A为对称矩阵的充分必要条件是AA^(T)A=A^(3).

Let A be a real matrix,then A is symmetric matrix if and only if AA^(T)=A^(T)A=A^(2).In this paper,we establish that A is a real symmetric matrix if and only if AA^(T)A=A^(3).