Results 241 to 250 of about 71,699 (272)

Inequalities on 2 × 2 block positive semidefinite matrices

Linear and multilinear algebra, 2021
We obtain two matrix inequalities on the off-diagonal block of 2 × 2 block positive semidefinite matrices and the geometric mean of its diagonal blocks. They improve some results of Lee [Linear Algebra Appl. 2015:486;449–453] and extend some inequalities
Xiaohui Fu, Pan-Shun Lau, T. Tam
semanticscholar   +1 more source

Transformation of non positive semidefinite correlation matrices

Communications in Statistics - Theory and Methods, 1993
In multivariate statistics, estimation of the covariance or correlation matrix is of crucial importance. Computational and other arguments often lead to the use of coordinate-dependent estimators, yielding matrices that are symmetric but not positive semidefinite.
Rousseeuw, Peter, Molenberghs, Geert
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Inequalities on partial traces of positive semidefinite block matrices

Canadian mathematical bulletin, 2020
Inequalities on partial traces of positive semidefinite matrices are studied. Extensions of several existing inequalities on the determinant of partial traces are then obtained.
Xiaohui Fu, Pan-Shun Lau, T. Tam
semanticscholar   +1 more source

Norm inequalities for positive semidefinite matrices

Wuhan University Journal of Natural Sciences, 2012
This paper aims to discuss some inequalities involving unitarily invariant norms and positive semidefinite matrices. By using properties of unitarily invariant norms, we obtain two inequities involving unitarily invariant norms and positive semidefinite matrices, which generalize the result obtained by Bhatia and Kittaneh.
Limin Zou, Yanqiu Wu
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Positive Semidefinite Matrices

1999
This chapter studies the positive semidefinite matrices, concentrating primarily on the inequalities of this type of matrix. The main goal is to present the fundamental results and show some often-used techniques. Section 7.1 gives the basic properties, Section 7.2 treats the L¨owner partial ordering of positive semidefinite matrices, and Section 7.3 ...
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Semidefinite Programming in the Space of Partial Positive Semidefinite Matrices

SIAM Journal on Optimization, 2003
Summary: We build upon the work of \textit{M. Fukuda} et al. [SIAM J. Optim. 11, 647--674 (2001; Zbl 1010.90053)] and \textit{K. Nakata} et al. [Math. Program. 95, No. 2(B), 303--327 (2003; Zbl 1030.90081)], in which the theory of partial positive semidefinite matrices was applied to the semidefinite programming (SDP) problem as a technique for ...
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Further unitarily invariant norm inequalities for positive semidefinite matrices

Positivity (Dordrecht), 2022
Ahmad Al-Natoor, F. Kıttaneh
semanticscholar   +1 more source

Singular value inequalities for convex functions of positive semidefinite matrices

Annals of Functional Analysis, 2022
Ahmad Al-Natoor, O. Hirzallah, F. Kıttaneh   +2 more
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A Hilbert-Schmidt norm Inequality for positive semidefinite matrices related to a question of Bourin

Positivity (Dordrecht), 2022
M. Hayajneh, Saja Hayajneh, F. Kıttaneh
semanticscholar   +1 more source

Spectral decomposition of selfadjoint matrices in positive semidefinite inner product spaces and its applications

Linear and multilinear algebra, 2018
Given a positive semidefinite matrix A, we obtain spectral decomposition of A-selfadjoint matrices which act on a positive semidefinite inner product space in which the inner product is induced by A.
T. Tam, Pingping Zhang
semanticscholar   +1 more source