A characterization of minimal Hermitian matrices

被引：17

作者：

Andruchow, E. ^{[1
,2
]}

Larotonda, G. ^{[1
,2
]}

Recht, L. ^{[3
]}

Varela, A. ^{[1
,2
]}

机构：

[1] Univ Natl Gen Sarmiento, Inst Ciencias, RA-1613 Los Polvorines, Argentina

[2] Consejo Nacl Invest Cient & Tecn, Inst Argentino Matemat IAM Alberto P Calderon, RA-1033 Buenos Aires, DF, Argentina

[3] Univ Simon Bolivar, Caracas 1080A, Venezuela

来源：

LINEAR ALGEBRA AND ITS APPLICATIONS | 2012年 / 436卷 / 07期

关键词：

Minimal Hermitian matrix; Diagonal matrix; Quotient operator norm; Best approximation;

D O I：

10.1016/j.laa.2011.08.042

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We describe properties of a Hermitian matrix M is an element of M-n (C) having minimal quotient norm in the following sense: parallel to M parallel to <= parallel to M + D parallel to for all real diagonal matrices D is an element of M-n(C). Here parallel to parallel to II denotes the operator norm. We show a constructive method to obtain all the minimal matrices of any size. (C) 2011 Elsevier Inc. All rights reserved.

引用

页码：2366 / 2374

页数：9

共 10 条

[1] Minimal matrices and the corresponding minimal curves on flag manifolds in low dimension
Andruchow, Esteban
Mata-Lorenzo, Luis E.
Mendoza, Alberto
Recht, Lazaro
Varela, Alejandro
[J]. LINEAR ALGEBRA AND ITS APPLICATIONS, 2009, 430 (8-9) : 1906 - 1928
[2] [Anonymous], 1958, J. Lond. Math. Soc., DOI [DOI 10.1112/JLMS/S1-33.1.14, 10.1112/jlms/s1-33.1.14]
[3] Bhatia Rajendra, 1997, Matrix Analysis: Graduate Texts in Mathematics, V169
[4] Generalized finite algorithms for constructing Hermitian matrices with prescribed diagonal and spectrum
Dhillon, IS
Heath, RW
Sustik, MA
Tropp, JA
[J]. SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS, 2005, 27 (01) : 61 - 71
[5] Metric geometry in homogeneous spaces of the unitary group of a C*-algebra:: Part I -: minimal curves
Durán, CE
Mata-Lorenzo, LE
Recht, L
[J]. ADVANCES IN MATHEMATICS, 2004, 184 (02) : 342 - 366
[6] Horn A., 1954, Am. J. Math., V76, P620, DOI DOI 10.2307/2372705
[7] Marshall A. W., 1979, MATH SCI ENG, V143
[8] Rieffel M.A., ARXIV10083733V4MATHO
[9] Defect of a unitary matrix
Tadej, Wojciech
Zyczkowski, Karol
[J]. LINEAR ALGEBRA AND ITS APPLICATIONS, 2008, 429 (2-3) : 447 - 481
[10] Random unistochastic matrices
Zyczkowski, K
Kus, M
Slomczynski, W
Sommers, HJ
[J]. JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL, 2003, 36 (12): : 3425 - 3450

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