This paper focuses on a matrix of elementary transformation in higher algebra, linear algebra and number theory in the elementary extensive use.

本论文主要论述了矩阵的初等变换在高等代数、线性代数以及初等数论中的广泛运用。

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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。

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