ON THE MINIMUM RANK AMONG POSITIVE SEMIDEFINITE MATRICES WITH A GIVEN GRAPH

被引：46

作者：

Booth, Matthew ^{[7
]}

Hackney, Philip ^{[2
]}

Harris, Benjamin ^{[3
]}

Johnson, Charles R. ^{[4
]}

Lay, Margaret ^{[5
]}

Mitchell, Lon H. ^{[6
]}

Narayan, Sivaram K. ^{[1
]}

Pascoe, Amanda ^{[8
]}

Steinmetz, Kelly ^{[9
]}

Sutton, Brian D. ^{[10
]}

Wang, Wendy ^{[11
]}

机构：

[1] Cent Michigan Univ, Dept Math, Mt Pleasant, MI 48859 USA

[2] Purdue Univ, Dept Math, W Lafayette, IN 47907 USA

[3] Brown Univ, Dept Math, Providence, RI 02912 USA

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

[5] Grinnell Coll, Dept Math & Comp Sci, Grinnell, IA 50112 USA

[6] Virginia Commonwealth Univ, Dept Math, Richmond, VA 23284 USA

[7] Oberlin Coll, Dept Math, Oberlin, OH 44074 USA

[8] Furman Univ, Dept Math, Greenville, SC 29613 USA

[9] Indiana Univ, Dept Math, Bloomington, IN 47405 USA

[10] Randolph Macon Coll, Dept Math, Ashland, VA 23005 USA

[11] Duke Univ, Dept Math, Durham, NC 27708 USA

来源：

SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS | 2008年 / 30卷 / 02期

基金：

美国国家科学基金会;

关键词：

rank; positive semidefinite; graph of a matrix;

D O I：

10.1137/050629793

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Let P(G) be the set of all positive semidefinite matrices whose graph is G, and msr(G) be the minimum rank of all matrices in P(G). Upper and lower bounds for msr(G) are given and used to determine msr(G) for some well-known graphs, including chordal graphs, and for all simple graphs on less than seven vertices.

引用

页码：731 / 740

页数：10

共 50 条

[21] A remark on the rank of positive semidefinite matrices subject to affine constraints
Barvinok, A
DISCRETE & COMPUTATIONAL GEOMETRY, 2001, 25 (01) : 23 - 31
[22] Four-dimensional polytopes of minimum positive semidefinite rank
Gouveia, Joao
Pashkovich, Kanstanstin
Robinson, Richard Z.
Thomas, Rekha R.
JOURNAL OF COMBINATORIAL THEORY SERIES A, 2017, 145 : 184 - 226
[23] SPARSITY PATTERNS WITH HIGH RANK EXTREMAL POSITIVE SEMIDEFINITE MATRICES
HELTON, JW
LAM, D
WOERDEMAN, HJ
SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS, 1994, 15 (01) : 299 - 312
[24] A SPARSE DECOMPOSITION OF LOW RANK SYMMETRIC POSITIVE SEMIDEFINITE MATRICES
Hou, Thomas Y.
Li, Qin
Zhang, Pengchuan
MULTISCALE MODELING & SIMULATION, 2017, 15 (01): : 410 - 444
[25] Correlation matrices, Clifford algebras, and completely positive semidefinite rank
Prakash, Anupam
Varvitsiotis, Antonios
LINEAR & MULTILINEAR ALGEBRA, 2020, 68 (05): : 1039 - 1056
[26] A NOTE ON THE POSITIVE SEMIDEFINITE MINIMUM RANK OF A SIGN PATTERN MATRIX
Cai, Xinzhong
Wang, Xinmao
ELECTRONIC JOURNAL OF LINEAR ALGEBRA, 2013, 26 : 345 - 356
[27] LOW-RANK OPTIMIZATION ON THE CONE OF POSITIVE SEMIDEFINITE MATRICES
Journee, M.
Bach, F.
Absil, P. -A.
Sepulchre, R.
SIAM JOURNAL ON OPTIMIZATION, 2010, 20 (05) : 2327 - 2351
[28] The minimum rank of symmetric matrices described by a graph: A survey
Fallat, Shaun M.
Hogben, Leslie
LINEAR ALGEBRA AND ITS APPLICATIONS, 2007, 426 (2-3) : 558 - 582
[29] Positive semidefinite rank
Hamza Fawzi
João Gouveia
Pablo A. Parrilo
Richard Z. Robinson
Rekha R. Thomas
Mathematical Programming, 2015, 153 : 133 - 177
[30] Positive semidefinite rank
Fawzi, Hamza
Gouveia, Joao
Parrilo, Pablo A.
Robinson, Richard Z.
Thomas, Rekha R.
MATHEMATICAL PROGRAMMING, 2015, 153 (01) : 133 - 177

← 1 2 3 4 5 →