Note on best possible bounds for determinants of matrices close to the identity matrix

被引：15

作者：

Brent, Richard P. ^{[1
]}

Osborn, Judy-anne H. ^{[2
]}

Smith, Warren D. ^{[3
]}

机构：

[1] Australian Natl Univ, Canberra, ACT 0200, Australia

[2] Univ Newcastle, Callaghan, NSW 2308, Australia

[3] Ctr Range Voting, Stony Brook, NY 11790 USA

来源：

LINEAR ALGEBRA AND ITS APPLICATIONS | 2015年 / 466卷

基金：

澳大利亚研究理事会;

关键词：

Determinant; Perturbation bound; Diagonally dominant matrix; Skew-Hadamard matrix; Fredholm determinant; Maximal determinant;

D O I：

10.1016/j.laa.2014.09.041

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We give upper and lower bounds on the determinant of a small perturbation of the identity matrix. The lower bounds are best possible, and in most cases they are stronger than well-known bounds due to Ostrowski and other authors. The upper bounds are best possible if a skew-Hadamard matrix of the same order exists. (C) 2014 Elsevier Inc. All rights reserved.

引用

页码：21 / 26

页数：6

共 14 条

[1]

[Anonymous], 1937, Commentarii Mathematici Helvetici

[2]

[Anonymous], 1991, Topics in Matrix Analysis, 1991

[3]

[Anonymous], 1893, Bull. des sciences math.

[4] Higher order derivatives and perturbation bounds for determinants [J].

Bhatia, Rajendra ;

Jain, Tanvi .

LINEAR ALGEBRA AND ITS APPLICATIONS, 2009, 431 (11) :2102-2108

[5]

Brent R.P., 2014, ARXIV14017048V7

[6]

Brent R.P., 2014, ARXIV14026817V2

[7]

Colbourn C. J., 2006, Handbook of Combinatorial Designs (Discrete Mathematics and Its Applications), V2nd

[8] Bounds for determinants of perturbed M-matrices [J].

Elsner, L .

LINEAR ALGEBRA AND ITS APPLICATIONS, 1997, 257 :283-288

[9]

Gerchgorin S., 1931, Izv. Akad. Nauk SSSR Ser. Mat, V6, P749

[10] PERTURBATION BOUNDS FOR DETERMINANTS AND CHARACTERISTIC POLYNOMIALS [J].

Ipsen, Ilse C. F. ;

Rehman, Rizwana .

SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS, 2008, 30 (02) :762-776

← 1 2 →