英语翻译幂零矩阵性质及应用摘要：幂零矩阵是一类特殊的矩阵,在矩阵理论中有重要的作用.它具有一些很好的性质.本文从矩阵的不同角度讨论了幂零矩阵的相关性质.幂零矩阵与若当形矩阵

Question

英语翻译
幂零矩阵性质及应用
摘要：幂零矩阵是一类特殊的矩阵,在矩阵理论中有重要的作用.它具有
一些很好的性质.本文从矩阵的不同角度讨论了幂零矩阵的相关性质.幂
零矩阵与若当形矩阵结合可得一个很好性质,在解相关矩阵问题有很好作
用,由此我们举例说明,从例子中发现了问题并对此问题进行思考得出了
一些结论,对幂零矩阵的研究很有意义.在一般矩阵中,求矩阵的逆比较
麻烦,本文最后利用幂零矩阵特殊性讨论了三类特殊矩阵逆的求法.
关键词：幂零矩阵 若当块 特征值 幂零指数

Answer 1

The Nature And Application Of Nilpotent Matrix
Summary:Nilpotent matrix is a special type of matrix that has an important place in matrix theory.It has some useful characteristics too.This article discusses some of the relevant characteristics from various perspectives.Nilpotent matrix can also be used in conjunction with Jordan matrix to facilitate solving relevant matrix problems.Illustrative examples have been provided in this article and a problem has been identified.By exploring this problem,conclusions are drawn,which are significant in the study of nilpotent matrix.Furthermore,nilpotent matrix can be used to simplify the usually clumsy process of finding the inverses of ordinary matrices.The last part of the article therefore discusses the approaches for finding inverses of three particular types of matix using the special characteristics of nilpotent matrix.
Keywords:nilpotent matrix,Jordan block,eigenvalue,nilpotent index