给出并证明了实幂等矩阵的九个等价条件，以及实对称幂等矩阵的一个等价条件。
Nine equivalent conditions of real idempotent matrix are given and proved, and one equivalent condition of real symmetric idempotent matrix is also given in this paper.
本文主要研究了符号幂等矩阵和对称符号模式矩阵的性质及它们之间的关系，特别是符号幂等矩阵的负元素的个数。
In this paper, we mainly study the sign idempotent of sign patterns, symmetric sign patterns and their relations, especially the number of negative entries that occur in sign idempotent sign pattern.
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