若当标准形理论在矩阵特征值问题上的应用.doc

若当标准形理论在矩阵特征值问题上的应用
The application of Jordan Standard Form theory in the issue of matrix eigenvalue

目 录

摘 要 I
Abstract I
引 言 1
第一章 矩阵的基本知识 2
1.1 矩阵等价和矩阵的秩 2
1.2 矩阵的特征值及特征向量和矩阵的相似 3
1.3 矩阵及矩阵的若当标准型 3
第二章 矩阵的若当标准型的常见应用 8
2.1 矩阵的若当标准型在矩阵分解上的应用 8
2.2 矩阵的若当标准型在矩阵秩的问题上的应用 11
第三章 矩阵的若当标准型在有关矩阵特征值问题上的应用 16
结论 26
致谢 27
参考文献 28



摘要 在高等代数中，比如线性方程问题，二次型问题以及线性空间的问题都运用到了矩阵的理论。本文主要简单介绍了矩阵的若当标准型理论在矩阵的分解以及矩阵秩的有关问题上的应用。着重探究了若当标准型理论在有关矩阵特征值方面的应用。通过几个典型的例子以及考研经常出现的题目进行讲解来对矩阵若当标准性能理论进行深一步地理解。

关键词：高等代数；若当标准形；矩阵； 等价；相似；特征值


The application of Jordan Standard Form theory in the issue of matrix eigenvalue
Abstract In advanced algebra , matrix theory and methods throughout the various aspects determinant of linear equations, many questions linear space, linear transformations , quadratic . There are of advanced algebra can be converted into the corresponding matrix problem to deal with . The theory of matrix is also in an important tool for research questions
of mathematics and science branch .
The theory of Jordan standard in matrix is an very important theory in advanced algebra. I discuss the theory in the aspect of rank matrix and the decomposition of matrix ,especially the applications in eigenvalues of the matrix .We want through a few typical examples and some questions which appeal in pubmed to understand the matrix theory deeply .

Keywords:advanced algebra; Jordan standard form; matrix; similar; equivalence; eigenvalues