Sylvester-Kac矩阵的可约性研究  

Reducible Property of the Sylvester-Kac Matrix

作　　者：田咏梅 秦建国 TIAN Yongmei;QIN Jianguo(General Education Center,Zhengzhou Business University,Gongyi 451200,Henan,China)

机构地区：[1]郑州商学院通识教育中心,河南巩义451200

出　　处：《山西师范大学学报(自然科学版)》2025年第1期26-29,共4页Journal of Shanxi Normal University(Natural Science Edition)

摘　　要：利用可约矩阵的概念与理论,研究了Sylvester-Kac矩阵PP~T的可约性,获得了矩阵P不可约而PP~T可约的结果.利用后者进一步将以P为系数矩阵的线性方程组Px=b的解的问题归结为两个阶数较低的线性方程组的解的问题.此外,还给出了一个可与对角矩阵相似却未必酉相似于对角矩阵的反例.The reducible properties of the Sylvester-Kac matrix Pand PPT are investigated by utilizing the concept and theory of reducible matrix.The results that P is irreducible and PPT is reducible are obtained.The solution problem of linear system Px=b is reduced in two linear systems which orders are lower than that of Px=b.In addition,a counterexample is given which can be similar but not necessarily unitary similar to a diagonal matrix.

关 键 词：Sylvester-Kac矩阵 不可约矩阵 线性方程组 

分 类 号：O151.21[理学—数学]