Optimal ellipsoids and decomposition of positive definite matrices

被引：1

作者：

Leung, Yuk J. ^{[1
]}

Li, Wenbo V. ^{[1
]}

Rakesh ^{[1
]}

机构：

[1] Univ Delaware, Dept Math Sci, Newark, DE 19716 USA

来源：

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 2007年 / 331卷 / 02期

基金：

美国国家科学基金会;

关键词：

ellipsoid; determinant maximization; John's theorem;

D O I：

10.1016/j.jmaa.2006.09.065

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Given a positive definite matrix A, we characterize the unique diagonal matrix D, D >= A, with the smallest determinant. Equivalently, given an ellipsoid A, we characterize the unique ellipsoid of the largest volume contained in A, with principal axes parallel to the coordinate axes. (c) 2006 Elsevier Inc. All rights reserved.

引用

页码：1452 / 1466

页数：15

共 50 条

[21] An inequality for positive definite matrices with applications to combinatorial matrices
Neubauer, MG
LINEAR ALGEBRA AND ITS APPLICATIONS, 1997, 267 : 163 - 174
[22] Information Geometry of Positive Definite Matrices
张士诚
孙华飞
李春辉
JournalofBeijingInstituteofTechnology, 2009, 18 (04) : 484 - 487
[23] NOTE ON EXTREME POSITIVE DEFINITE MATRICES
CHRISTENSEN, JPR
VESTERSTROM, J
MATHEMATISCHE ANNALEN, 1979, 244 (01) : 65 - 68
[24] Interacting diffusions on positive definite matrices
O'Connell, Neil
PROBABILITY THEORY AND RELATED FIELDS, 2021, 180 (3-4) : 679 - 726
[25] DETERMINANTAL INEQUALITIES OF POSITIVE DEFINITE MATRICES
Choi, Daeshik
MATHEMATICAL INEQUALITIES & APPLICATIONS, 2016, 19 (01): : 167 - 172
[26] A DETERMINANTAL INEQUALITY FOR POSITIVE DEFINITE MATRICES
Lin, Minghua
ELECTRONIC JOURNAL OF LINEAR ALGEBRA, 2014, 27 : 821 - 826
[27] Products of positive definite symplectic matrices
Granario, Daryl Q.
Tam, Tin-Yau
LINEAR ALGEBRA AND ITS APPLICATIONS, 2021, 626 : 188 - 203
[28] Subdivision Schemes for Positive Definite Matrices
Uri Itai
Nir Sharon
Foundations of Computational Mathematics, 2013, 13 : 347 - 369
[29] INEQUALITIES FOR POSITIVE DEFINITE SYMMETRIC MATRICES
MAN, FT
SIAM JOURNAL ON APPLIED MATHEMATICS, 1970, 19 (04) : 679 - &
[30] AN ADAPTIVE FAST SOLVER FOR A GENERAL CLASS OF POSITIVE DEFINITE MATRICES VIA ENERGY DECOMPOSITION
Hou, Thomas Y.
Huang, De
Lam, Ka Chun
Zhang, Pengchuan
MULTISCALE MODELING & SIMULATION, 2018, 16 (02): : 615 - 678

← 1 2 3 4 5 →