Linear maps leaving invariant subsets of nonnegative symmetric matrices

被引：2

作者：

Chiang, HL ^{[1
]}

Li, CK ^{[1
]}

机构：

[1] Coll William & Mary, Dept Math, Williamsburg, VA 23187 USA

来源：

BULLETIN OF THE AUSTRALIAN MATHEMATICAL SOCIETY | 2003年 / 68卷 / 02期

关键词：

D O I：

10.1017/S0004972700037618

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let S be a certain set of nonnegative symmetric matrices, such as the set of symmetric doubly stochastic matrices or the set, of symmetric permutation matrices. It is proven that a linear transformation mapping S onto S must be of the form X --> P-t X P for some permutation matrix P except for several low dimensional cases.

引用

页码：221 / 231

页数：11

共 50 条

[1] Linear maps on nonnegative symmetric matrices preserving the independence number
Hu, Yanan
Huang, Zejun
[J]. LINEAR ALGEBRA AND ITS APPLICATIONS, 2023, 670 : 154 - 167
[2] Linear maps leaving the alternating group invariant
Chiang, H
Li, CK
[J]. LINEAR ALGEBRA AND ITS APPLICATIONS, 2002, 340 : 69 - 80
[3] Symmetric arctic ranks of nonnegative matrices and their linear preservers
Beasley, LeRoy B.
Song, Seok-Zun
[J]. LINEAR & MULTILINEAR ALGEBRA, 2017, 65 (10): : 2000 - 2010
[4] Dynamics of piecewise linear maps and sets of nonnegative matrices
Bondarenko, Ievgen
[J]. LINEAR ALGEBRA AND ITS APPLICATIONS, 2009, 431 (5-7) : 495 - 510
[5] LINEAR MAPS ON MATRICES - INVARIANCE OF SYMMETRIC POLYNOMIALS
RACKUSIN, J
WATKINS, W
[J]. LINEAR ALGEBRA AND ITS APPLICATIONS, 1977, 17 (03) : 269 - 276
[6] On linear maps leaving invariant the copositive/completely positive cones
Jayaraman, Sachindranath
Mer, Vatsalkumar N.
[J]. CZECHOSLOVAK MATHEMATICAL JOURNAL, 2024,
[7] Nonnegative Eigenvectors of Symmetric Matrices
Swan, Hunter
[J]. AMERICAN MATHEMATICAL MONTHLY, 2019, 126 (06): : 559 - 560
[8] 2 INEQUALITIES IN NONNEGATIVE SYMMETRIC MATRICES
LONDON, D
[J]. PACIFIC JOURNAL OF MATHEMATICS, 1966, 16 (03) : 515 - &
[9] DAD THEOREM FOR SYMMETRIC NONNEGATIVE MATRICES
CSIMA, J
DATTA, BA
[J]. CANADIAN MATHEMATICAL BULLETIN, 1969, 12 (05): : 697 - &
[10] DAD THEOREM FOR SYMMETRIC NONNEGATIVE MATRICES
CSIMA, J
DATTA, BN
[J]. NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY, 1970, 17 (01): : 255 - &

← 1 2 3 4 5 →