LOWER BOUNDS FOR THE SPREAD OF A NONNEGATIVE MATRIX

被引：3
|
作者：
Drnovsek, Roman [1 ]
机构：
[1] Univ Ljubljana, Fac Math & Phys, Dept Math, Jadranska 19, SI-1000 Ljubljana, Slovenia
来源：
MATHEMATICAL INEQUALITIES & APPLICATIONS | 2021年 / 24卷 / 03期
关键词：
Nonnegative matrices; spectrum; spread; spectral radius;
D O I：
10.7153/mia-2021-24-55
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
Given an integer n >= 2 and a real number a >= 0, let C-n(a) be the collection of all nonnegative n x n matrices A = [a(i, j)](i, j=1)(n) such that a = min(1 <= i <= n) a(i, i) and r(A) > a, where r(A) denotes the spectral radius of A. We prove some lower bounds for the spread s(A) of A subset of C-n(a) that is defined as the maximum distance between any two eigenvalues of A. In particular, we prove that s(A) > 2/2+root 2n (r(A) - a) for all A is an element of C-n(a).
引用
收藏
页码：793 / 799
页数：7
相关论文
共 50 条
12345