This paper obtained the following results: a simple solution for the similarity matrix under a similarity transformation is obtained by using a matrix polynomial.
本文得到下列结果：通过应用矩阵多项式，得到一个相似变换下变换矩阵的简便解法。
In this paper we get a seeking unified method of the least common multiple the greatest common factor and coefficients polynomial by implementing elementary row transformation in a polynomial matrix.
利用矩阵的初等变换，给出了两个多项式的最小公倍式、最大公因式及其系数多项式的统一求法。
In this paper by using the symplectic transformation condition, some new formulas including Chebyshev Polynomial, trigonometric identity, hyperbolic identity were obtained.
利用辛变换条件得到了一些新的切比雪夫多项式公式、三角恒等式和双曲恒等式。
The property of companion matrix is studied, and the method of calculating the characteristic polynomial of matrix with similar transformation is explained.
研究了友阵的性质，论述了用相似变换计算矩阵特征多项式的方法。
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。
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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