矩阵能量与其迹的关系研究  

Relationship between matrix energy and its traces

作　　者：金旭梅 李崇民 李静 JIN Xu-mei;LI Chong-min;LI Jing(College of Mathematics and Statistics,Qinghai Normal University,Xining 810016,China)

机构地区：[1]青海师范大学数学与统计学院,青海西宁810016

出　　处：《青海师范大学学报（自然科学版）》2022年第4期20-24,共5页Journal of Qinghai Normal University(Natural Science Edition)

基　　金：青海省科技厅资助项目(2022-ZJ-T02);青海省部共建藏语智能信息处理及应用国家重点实验室;藏文信息处理教育部重点实验室;青海人民政府—北京师范大学高原科学与可持续发展研究院;111引智计划(D20035)

摘　　要：迹作为矩阵的一个重要的相似不变量,与矩阵的特征根的相关不变量存在密切联系.国外学者Rada利用矩阵的迹研究了关于有向图邻接矩阵的迹与特征根的关系,获得了关于有向图能量紧的下界.本文定义矩阵的能量为矩阵特征根的实部之和,把有向图能量推广到更一般的情形.通过二次型展开式和实部与虚部的比较等方式,深入探讨了矩阵特征根与迹的关系,获得若干用矩阵的迹来表示的矩阵能量的下界.基于矩阵能量与其迹的关系,本文展示了矩阵能量在简单图和有向图中的应用.In this work,matrix energy is defined as the sum of absolute values of real parts of its eigenvalues.By using quadratic expansion and comparing the real parts and imaginary ones,the relationship between traces and its energy of a matrix is deep explored,and several lower bounds of matrix energy in term of traces of a matrix are obtained.Based on the relationship between matrix energy and its trace,the applications of matrix energy in simple graphs and directed graphs are shown.

关 键 词：矩阵能量 实特征根 复特征根 矩阵的迹 

分 类 号：O157.5[理学—数学]