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

Richard P. Brent; Judy Anne H. Osborn; Warren D. Smith

doi:10.1016/j.laa.2014.09.041

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

Richard P. Brent^*
, Judy Anne H. Osborn
, Warren D. Smith

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

15 Citations (Scopus)

Abstract

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.

Original language	English
Pages (from-to)	21-26
Number of pages	6
Journal	Linear Algebra and Its Applications
Volume	466
DOIs	https://doi.org/10.1016/j.laa.2014.09.041
Publication status	Published - 1 Feb 2015

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title = "Note on best possible bounds for determinants of matrices close to the identity matrix",

abstract = "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.",

keywords = "Determinant, Diagonally dominant matrix, Fredholm determinant, Maximal determinant, Perturbation bound, Skew-Hadamard matrix",

author = "Brent, \{Richard P.\} and Osborn, \{Judy Anne H.\} and Smith, \{Warren D.\}",

note = "Publisher Copyright: {\textcopyright} 2014 Elsevier Inc.",

year = "2015",

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doi = "10.1016/j.laa.2014.09.041",

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AU - Brent, Richard P.

AU - Osborn, Judy Anne H.

AU - Smith, Warren D.

PY - 2015/2/1

Y1 - 2015/2/1

N2 - 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.

AB - 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.

KW - Determinant

KW - Diagonally dominant matrix

KW - Fredholm determinant

KW - Maximal determinant

KW - Perturbation bound

KW - Skew-Hadamard matrix

UR - https://www.scopus.com/pages/publications/84908426097

U2 - 10.1016/j.laa.2014.09.041

DO - 10.1016/j.laa.2014.09.041

M3 - Article

SN - 0024-3795

VL - 466

SP - 21

EP - 26

JO - Linear Algebra and Its Applications

JF - Linear Algebra and Its Applications

ER -

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

Abstract

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