利用线性变换及方阵Jordan标准型的方法，给出了Stein矩阵方程存在唯一解的充分必要条件以及解的形式。采用的方法是初等的，所得的结果比已有结论丰富。该方法也可用来研究一般域上的矩阵方程，从而为研究密码学基础理论提供一种新方法。关 键 词 矩阵; Jordan标准型; Stein方程; 线性变换Abstract Using the linear transformation method, this paper gives the necessary and sufficient conditions for Stein equation to have unique solution .The unique solution is also obtained. The method in this paper is elementary and the results are richer than the conclusion quoted from the references of this pojoer. The method in this paper can also be used to deal with mtrix equations on general field, which supplies a new method to cryptography.Key words matrix; Jordan form; Stein equation; linear transformation
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