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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应注意在构造ARMA新息模型时，必须进行多项式矩阵的左素分解，才能得到正确的ARMA新息模型。

Notice that constructing the ARMA innovation model, a left co-prime factorization to a polynomial matrix must be performed, so that the ARMA innovation model can correctly be obtained.

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