Results 11 to 20 of about 2,883,021 (288)
Decompositions of minimum rank matrices
Linear Algebra and its Applications, 2013 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
W. Barrett +5 more
semanticscholar +3 more sources
Minimum rank of powers of trees [PDF]
The Electronic Journal of Linear Algebra, 2012 The minimum rank of a simple graph G over a field F is the smallest possible rank among all real symmetric matrices, over F, whose (i, j)-entry (for i 6= j) is nonzero whenever ij is an edge in G and is zero otherwise.
Luz M. DeAlba +5 more
semanticscholar +2 more sources
, 2013 Haemers’ minimum rank, η(G), was first defined by Willem Haemers in 1979. He created this graph parameter as an upper bound for the Shannon capacity of a graph, Θ(G), and to answer some questions asked by Lovasz in his famous paper where he determined Θ(C5) = √ 5.
Geoff Tims
semanticscholar +3 more sources
ADMiRA: Atomic Decomposition for Minimum Rank Approximation [PDF]
IEEE Transactions on Information Theory, 2010 A short version (arXiv:0901.1898) will be presented at ISIT ...
Kiryung Lee, Yoram Bresler
exaly +3 more sources
Minimum rank of outerplanar graphs
Linear Algebra and its Applications, 2012 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
J. Sinkovic, Mark Kempton
semanticscholar +3 more sources
Approximating the minimum rank of a graph via alternating projection
Operations Research Letters, 2016 Franklin Kenter
exaly +2 more sources
Bounds on the Minimum Edge Dominating Energy in Terms of Some Parameters of a Graph [PDF]
Mathematics Interdisciplinary Research, 2023 The minimum edge dominating energy, denoted by $EE_{F}(G)$, is the sum of the absolute values of eigenvalues of the minimum edge dominating matrix of graph $G$.
Fateme Movahedi
doaj +1 more source
Sum-rank product codes and bounds on the minimum distance [PDF]
Finite Fields Their Appl., 2021 The tensor product of one code endowed with the Hamming metric and one endowed with the rank metric is analyzed. This gives a code which naturally inherits the sum-rank metric.
Gianira N. Alfarano +3 more
semanticscholar +1 more source
Guaranteed Minimum-Rank Solutions of Linear Matrix Equations via Nuclear Norm Minimization [PDF]
SIAM Review, 2007 The affine rank minimization problem consists of finding a matrix of minimum rank that satisfies a given system of linear equality constraints. Such problems have appeared in the literature of a diverse set of fields including system identification and ...
B. Recht, Maryam Fazel, P. Parrilo
semanticscholar +1 more source
Polytopes of Minimum Positive Semidefinite Rank [PDF]
Discrete & Computational Geometry, 2013 The positive semidefinite (psd) rank of a polytope is the smallest $k$ for which the cone of $k \times k$ real symmetric psd matrices admits an affine slice that projects onto the polytope. In this paper we show that the psd rank of a polytope is at least the dimension of the polytope plus one, and we characterize those polytopes whose psd rank equals ...
João Gouveia +2 more
openaire +3 more sources