A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2019; you can also visit the original URL.
The file type is `application/pdf`

.

## Filters

##
###
Completely positive semidefinite rank

2017
*
Mathematical programming
*

First, the cpsd-

doi:10.1007/s10107-017-1198-4
fatcat:zh7h7tje2nffdkgrbpbi2eojei
*rank*is a natural non-commutative analogue of the*completely**positive**rank*of a*completely**positive*matrix. ... An n× n matrix X is called*completely**positive**semidefinite*(cpsd) if there exist d× d Hermitian*positive**semidefinite*matrices {P_i}_i=1^n (for some d> 1) such that X_ij= Tr(P_iP_j), for all i,j ∈{ 1, ...*semidefinite*cone (resp.*completely**positive*cone). ...##
###
Approximate Completely Positive Semidefinite Rank
[article]

2020
*
arXiv
*
pre-print

In this paper we provide an approximation for

arXiv:2012.06471v2
fatcat:ek46dxel2bhc7iwqqn7ommtc44
*completely**positive**semidefinite*(cpsd) matrices with cpsd-*rank*bounded above (almost) independently from the cpsd-*rank*of the initial matrix. ... We then employ the Johnson-Lindenstrauss Lemma to improve to a logarithmic dependence of the cpsd-*rank*on the size. ... Our main result yields an approximation of*completely**positive**semidefinite*matrices of relatively small*completely**positive**semidefinite**rank*. ...##
###
Matrices with high completely positive semidefinite rank

2017
*
Linear Algebra and its Applications
*

We construct

doi:10.1016/j.laa.2016.10.015
fatcat:h6mf372z6needfeaznss2ffcqm
*completely**positive**semidefinite*matrices of size 4k^2+2k+2 with complex*completely**positive**semidefinite**rank*2^k for any*positive*integer k. ... We also exhibit a class of*completely**positive*matrices with quadratic (in terms of the matrix size)*completely**positive**rank*, but with linear*completely**positive**semidefinite**rank*, and we make a connection ... The*completely**positive*and*completely**positive**semidefinite**ranks*are symmetric analogs of the nonnegative and*positive**semidefinite**ranks*. ...##
###
Correlation matrices, Clifford algebras, and completely positive semidefinite rank
[article]

2018
*
arXiv
*
pre-print

Using this we give a self-contained and succinct proof of the existence of

arXiv:1702.06305v2
fatcat:g3qqobyupvehxeynelhhaxa7la
*completely**positive**semidefinite*matrices with sub-exponential cpsd-*rank*, recently derived in the literature. ... We show that for extremal correlations, the matrices in such a factorization generate a Clifford algebra and thus, their size is exponential in terms of the*rank*of the correlation matrix. ... The*completely**positive**semidefinite**rank*of X ∈ CS n + , denoted by cpsd-*rank*(X), is defined as the least d ≥ 1 for which there exist d × d Hermitian*positive**semidefinite*matrices P 1 , . . . , P n satisfying ...##
###
Complexity of the positive semidefinite matrix completion problem with a rank constraint
[article]

2012
*
arXiv
*
pre-print

*completed*to a

*positive*

*semidefinite*matrix of

*rank*at most k. ... We consider the decision problem asking whether a partial rational symmetric matrix with an all-ones diagonal can be

*completed*to a full

*positive*

*semidefinite*matrix of

*rank*at most k. ... entries are all equal to 1, that can be

*completed*to a

*positive*

*semidefinite*matrix. ...

##
###
A new graph parameter related to bounded rank positive semidefinite matrix completions
[article]

2012
*
arXiv
*
pre-print

to edges of G, can be

arXiv:1204.0734v1
fatcat:y7eue5ijkrejzg2j7dz5uy7aue
*completed*to a*positive**semidefinite*matrix of*rank*at most k (assuming a*positive**semidefinite**completion*exists). ... The Gram dimension (G) of a graph G is the smallest integer k> 1 such that any partial real symmetric matrix, whose entries are specified on the diagonal and at the off-diagonal*positions*corresponding ... The problem of*completing*a partial matrix to a full*positive**semidefinite*(psd) matrix is one of the most extensively studied matrix*completion*problems. ...##
###
A new graph parameter related to bounded rank positive semidefinite matrix completions

2013
*
Mathematical programming
*

to edges of G, can be

doi:10.1007/s10107-013-0648-x
fatcat:fcsomo7egnh6dpqmm76x2slqmi
*completed*to a*positive**semidefinite*matrix of*rank*at most k (assuming a*positive**semidefinite**completion*exists). ... The Gram dimension gd(G) of a graph G is the smallest integer k ≥ 1 such that any partial real symmetric matrix, whose entries are specified on the diagonal and at the off-diagonal*positions*corresponding ... The problem of*completing*a partial matrix to a full*positive**semidefinite*(psd) matrix is one of the most extensively studied matrix*completion*problems. ...##
###
Complexity of the Positive Semidefinite Matrix Completion Problem with a Rank Constraint
[chapter]

2013
*
Fields Institute Communications
*

can be

doi:10.1007/978-3-319-00200-2_7
fatcat:5mpvfe5zkfhahjyfii7ut3jw2a
*completed*to a*positive**semidefinite*matrix of*rank*at most k. ... We consider the decision problem asking whether a partial rational symmetric matrix with an all-ones diagonal can be*completed*to a full*positive**semidefinite*matrix of*rank*at most k. ... entries are all equal to 1, that can be*completed*to a*positive**semidefinite*matrix. ...##
###
A Riemannian geometry with complete geodesics for the set of positive semidefinite matrices of fixed rank

2012
*
IMA Journal of Numerical Analysis
*

We present a homogeneous space geometry for the manifold of symmetric

doi:10.1093/imanum/drs006
fatcat:jeu2kstwcfcivl4u27twivg3ky
*positive**semidefinite*matrices of fixed*rank*. ... Abstract We present a homogeneous space geometry for the manifold of symmetric*positive**semidefinite*matrices of fixed*rank*. ... Sepulchre for helpful discussions about the geometry of fixed-*rank*matrices. ...##
###
Positive semidefinite completions of partial Hermitian matrices

1992
*
Linear Algebra and its Applications
*

We classify the

doi:10.1016/0024-3795(92)90304-s
fatcat:p4r6iihjnff5tgewi2ngpie2eu
*ranks*of*positive**semidefinite**completions*of Hermitian band matrices and other partially specified Hermitian matrices with chordal graphs and specified main diagonals. ...*Completing*a partially specified matrix means filling in the unspecified entries. ... there are exactly 2" real symmetric*positive**semidefinite**completions*F of R such that*Rank*F =*Rank*R. ...##
###
Matrix completion and semidefinite matrices
[article]

2021
*
arXiv
*
pre-print

*Positive*

*semidefinite*Hermitian matrices that are not fully specified can be

*completed*provided their underlying graph is chordal. ... For a class of matrices that are singular but of maximal

*rank*unique characterizations can be given, just as in the

*positive*definite case. ... We have shown in the last theorem that H is

*positive*

*semidefinite*if we set X = BC + D. H is also of maximal

*rank*. In general we have

*rank*H ≤

*rank*A +

*rank*C +

*rank*E. ...

##
###
A New Algorithm for Positive Semidefinite Matrix Completion

2016
*
Journal of Applied Mathematics
*

*Positive*

*semidefinite*matrix

*completion*(PSDMC) aims to recover

*positive*

*semidefinite*and low-

*rank*matrices from a subset of entries of a matrix. ... This task can be conducted by solving the nuclear norm regularized linear least squares model with

*positive*

*semidefinite*constraints. ... Acknowledgments The authors would like to thank Professor Zaiwen Wen for the discussions on matrix

*completion*. They thank Professor Xiaoming Yuan for offering the original codes of ADMM-VI. ...

##
###
Positive semidefinite maximum nullity and zero forcing number

2012
*
The Electronic Journal of Linear Algebra
*

In addition, this technique was used in [3] to establish the minimum

doi:10.13001/1081-3810.1559
fatcat:yxecfsv6ube2lmnhzddsadt4lq
*rank*of the*complete*ciclo C t (K r ), which is in fact the minimum*positive**semidefinite**rank*. ... The minimum*positive**semidefinite**rank*of G is the smallest possible*rank*over all real*positive**semidefinite*matrices described by G and the minimum Hermitian*positive**semidefinite**rank*of G is the smallest ...##
###
Semidefiniteness without real symmetry

2000
*
Linear Algebra and its Applications
*

part, and A 2 has

doi:10.1016/s0024-3795(99)00256-6
fatcat:bdlmcw3vybcmhmsowq4rxezt6q
*positive**semidefinite*symmetric part, then*rank*[AX] =*rank*[X T AX] for all X ∈ M n (R). ... . , A k (k 2) all have*positive**semidefinite*symmetric part, then*rank*[AX] =*rank*[X T AX] = · · · =*rank*[X T A k−1 X] for all X ∈ M n (R). ... Finally, as in the proof of Theorem 4,*rank*[X T A k−1 X] =*rank*[AX], and the induction step is*complete*. ...##
###
A direct proof for the matrix decomposition of chordal-structured positive semidefinite matrices

2010
*
Linear Algebra and its Applications
*

This decomposition is recently exploited to solve

doi:10.1016/j.laa.2010.04.012
fatcat:jkn36a2c4zaalh74wfho4l73pq
*positive**semidefinite*programming efficiently. ... Agler, Helton, McCullough, and Rodman proved that a graph is chordal if and only if any*positive**semidefinite*(PSD) symmetric matrix, whose nonzero entries are specified by a given graph, can be decomposed ... The matrix L is nonsingular and A is*positive**semidefinite*, which implies that X and A are both*positive**semidefinite*. ...
« Previous

*Showing results 1 — 15 out of 24,154 results*