等价关系的判定及性质

Diagnosis and Nature of the Equivalence Relation

设R是集合A上的二元关系,要判定R在A上是否是等价关系,一般来讲,只能从定义出发,当R包含的序偶较多时,从定义出发又比较难于判定.从关系矩阵出发,给出一种判定方法,并讨论等价关系的矩阵性质.

Suppose R has the binary relation with the set A, and to judge whether R has the equivalent relationship with A, in general we can decide it by definition. However, it will be difficult for this method to work if R contains lots of ordered pairs. In this paper, a diagnosis method based on relational matrix is given, and the matrix nature of equivalence relaiton is discussed.