若尔当标准形计算方法的注记与修正  

Notes and modifications to the calculation method of Jordan canonical form

作　　者：张盛[1] ZHANG Sheng(College of Mathematical Sciences,Bohai University,Jinzhou 121013,China)

机构地区：[1]渤海大学数学科学学院,辽宁锦州121013

出　　处：《渤海大学学报（自然科学版）》2022年第2期155-161,共7页Journal of Bohai University:Natural Science Edition

基　　金：国家自然科学基金项目(No:11547005);辽宁省教育厅项目(No:LJ20200021).

摘　　要：结合一个实例指出了文献[8]中关于若尔当标准形计算方法的值得注意之处,并给出了相应的修正.为验证修正方法的有效性,本文列举了四个实际算例.修正方法的优点在于嵌入的条件方程解决了文献[8]中方法在确定根子空间循环基过程中因对应线性方程组基础解系的选择不当而无法得到循环基的共性问题,以达到最终顺利求得若尔当标准形所对应的可逆矩阵之目的.算例表明,以统一方式嵌入联系于循环基对应线性方程组中的条件方程有时会出现被约化掉的现象,从中揭示出产生循环基的基础解系具有选择上的任意性,反之则不然.Combined with an example,the notable points on the calculation method of Jordan canonical form in[8]are pointed out,and the corresponding modifications are given.In order to verify the effectiveness of the modified method,four practical examples are given in this paper.The advantage of the modified method is that the embedded conditional equation solves the common problem that the cyclic basis cannot be obtained due to the improper selection of the system of fundamental solutions of the corresponding linear equations in the process of determining the cyclic basis in the root subspace,so as to achieve the purpose of successfully obtaining the reversible matrix corresponding to the Jordan canonical form.The examples show that the conditional equation embedded in the linear equations corresponding to the cyclic basis in a unified way is sometimes reduced,which reveals that the system of fundamental solutions generating the cyclic basis is arbitrary in selection,otherwise it is not.

关 键 词：若尔当标准形 可逆矩阵 循环基 特征值 基础解系 初等因子 

分 类 号：O151.21[理学—数学]