若當(dāng)標(biāo)準(zhǔn)形理論在矩陣特征值問題上的應(yīng)用
The application of Jordan Standard Form theory in the issue of matrix eigenvalue

目 錄

摘 要 I
Abstract I
引 言 1
第一章 矩陣的基本知識 2
1.1 矩陣等價和矩陣的秩 2
1.2 矩陣的特征值及特征向量和矩陣的相似 3
1.3 矩陣及矩陣的若當(dāng)標(biāo)準(zhǔn)型 3
第二章 矩陣的若當(dāng)標(biāo)準(zhǔn)型的常見應(yīng)用 8
2.1 矩陣的若當(dāng)標(biāo)準(zhǔn)型在矩陣分解上的應(yīng)用 8
2.2 矩陣的若當(dāng)標(biāo)準(zhǔn)型在矩陣秩的問題上的應(yīng)用 11
第三章 矩陣的若當(dāng)標(biāo)準(zhǔn)型在有關(guān)矩陣特征值問題上的應(yīng)用 16
結(jié)論 26
致謝 27
參考文獻 28



摘要 在高等代數(shù)中，比如線性方程問題，二次型問題以及線性空間的問題都運用到了矩陣的理論。本文主要簡單介紹了矩陣的若當(dāng)標(biāo)準(zhǔn)型理論在矩陣的分解以及矩陣秩的有關(guān)問題上的應(yīng)用。著重探究了若當(dāng)標(biāo)準(zhǔn)型理論在有關(guān)矩陣特征值方面的應(yīng)用。通過幾個典型的例子以及考研經(jīng)常出現(xiàn)的題目進行講解來對矩陣若當(dāng)標(biāo)準(zhǔn)性能理論進行深一步地理解。

關(guān)鍵詞：高等代數(shù)；若當(dāng)標(biāo)準(zhǔn)形；矩陣； 等價；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