矩阵多项式的性质讨论毕业论文.doc

1 矩阵多项式的性质讨论摘要: 本文系统总结了矩阵多项式的一些性质, 且主要针对矩阵多项式的特征值、秩、逆矩阵求法和可逆性判别、迹的性质的探讨以及矩阵多项式在代数学中的应用。其中对于已有的结论则不予证明,同时本文也给出了一些重要的结论。关键词:矩阵多项式特征多项式最小多项式特征值秩迹 Matrix to discuss the nature of polynomial Abstract : This article summarizes the matrix system polynomial some properties, mainly against Matrix and the characteristics of polynomials, rank, the matrix inverse discrimination law and reversible, track and investigate the nature of the matrix in polynomial The application of algebra. For the conclusions of which have not proved it, and this also gives a number of important conclusions. Key word s: Matrix polynomial characteristic polynomial smallest trace polynomial characteristics rank envalue. 2 目录 1引言......................................................................................................................................... 3 2矩阵多项式的基本性质......................................................................................................... 3 矩阵多项式的特征值.................................................................................................... 3 矩阵多项式的秩............................................................................................................ 5 矩阵多项式可逆判定与求法总结............................................................................... 7 矩阵多项式的迹.......................................................................................................... 10 3矩阵多项式性质的应用....................................................................................................... 13 矩阵多项式成为恒等式的应用.................................................................................. 13 矩阵多项式在求变换矩阵中的应用.......................................................................... 14 参考文献................................................................................................................................... 18 谢辞.........................................................................................................................