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.
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。
In this paper, we have discussed root subspace decomposition of linear space, and for the linear space have decomposed direct sum of root subspace, a primary proof is given.
文章讨论了线性空间的根子空间分解，并对线性空间分解成根子空间的直和给出了较为初等的证明。
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