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.
其主要思想是通过引入线性变换矩阵来近似经典的局部线性嵌入(LLE)，然后通过核方法的技巧在高维空间里求解。
The main idea is to approximate the classical local linear embedding (LLE) by introducing a linear transformation matrix and then find the solution in a very high dimensional space by kernel trick.
给出了线性变换的值域与核的和是直和的充要条件，并由此得到五个推论。
This paper presents that the sum of the value register of linear transformation and thenucleus is a full and necessary condition for direct sum, and from which five inductions are obtained.
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