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.

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给出了两两互素多项式下线性变换的核的直和分解，并应用于幂等矩阵（对合矩阵）的秩的等式证明中。

The direct sum decomposition of the addition of a linear transformation under the coprime polynomial was given, and it was used in the proof of some equality about the rank of idempotent matrix.

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讨论了一般符号模式矩阵的幂等性和广义逆。

I discuss idempotent, generalized inverses of general sign pattern matrix.

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