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

页码：793 / 799

页数：7

共 50 条

[21] Bounds for the greatest characteristic root of a nonnegative matrix
Liu, SL
LINEAR ALGEBRA AND ITS APPLICATIONS, 1996, 239 : 151 - 160
[22] Sharp bounds on the spectral radius of a nonnegative matrix
Duan, Xing
Zhou, Bo
LINEAR ALGEBRA AND ITS APPLICATIONS, 2013, 439 (10) : 2961 - 2970
[23] BOUNDS FOR MAXIMAL EIGENVALUE OF A NONNEGATIVE IRREDUCIBLE MATRIX
HALL, CA
PORSCHING, TA
DUKE MATHEMATICAL JOURNAL, 1969, 36 (01) : 159 - +
[24] New bounds for perron root of a nonnegative matrix
Chen J.
Li W.
Journal of Applied Mathematics and Computing, 2007, 23 (1-2) : 337 - 344
[25] NESTED BOUNDS FOR THE PERRON ROOT OF A NONNEGATIVE MATRIX
DEUTSCH, E
WIELANDT, H
LINEAR ALGEBRA AND ITS APPLICATIONS, 1983, 52-3 (JUL) : 235 - 251
[26] New Bounds For Perron Root of A Nonnegative Matrix
Li, Hua
Diao, Qun
ICMS2010: PROCEEDINGS OF THE THIRD INTERNATIONAL CONFERENCE ON MODELLING AND SIMULATION ICMS2010, VOL 5: APPLIED MATHEMATICS AND MATHEMATICAL MODELLING, 2010, : 92 - 96
[27] Lower bounds for the spread of normal matrices
Yu, Yisheng
Gu, Dunhe
Nanjing Li Gong Daxue Xuebao/Journal of Nanjing University of Science and Technology, 1994, (03):
[28] Lower bounds on the Laplacian spread of a graph
Lin, Zhen
Miao, Lianying
ARS COMBINATORIA, 2020, 151 : 221 - 230
[29] New lower bounds for the Randic spread
Andrade, Enide
de Freitas, Maria Aguieiras A.
Robbiano, Maria
Rodriguez, Jonnathan
LINEAR ALGEBRA AND ITS APPLICATIONS, 2018, 544 : 254 - 272
[30] Lower bounds on nonnegative signed domination parameters in graphs
Ghameshlou, Arezoo. N.
AKCE INTERNATIONAL JOURNAL OF GRAPHS AND COMBINATORICS, 2020, 17 (01) : 503 - 509

← 1 2 3 4 5 →