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Norm inequalities for positive semidefinite matrices
Wuhan University Journal of Natural Sciences, 2012This 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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Remarks on a Question of Bourin for Positive Semidefinite Matrices
Results in Mathematics, 2023For positive semidefinite matrices \(A\) and \(B\) over the field of complex numbers, the authors prove the norm inequalities \[ |||A^tB^{1-t}+B^tA^{1-t}|||\leq 2^{2(t-3/4)}|||A+B||| , \] if \(t\in [3/4,1]\) and \[ |||A^tB^{1-t}+B^tA^{1-t}|||\leq 2^{2(1/4-t)}|||A+B||| , \] if \(t\in [0,1/4].\) Here, \(|||\cdot |||\) is any unitarily invariant norm.
Hayajneh, Mostafa +2 more
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Completions of positive semidefinite operator matrices [PDF]
, 2011 This chapter deals with positive definite and semidefinite completions of partial operator matrices. It considers the banded case in Section 2.1, the chordal case in Section 2.2, the Toeplitz case in Section 2.3, and the generalized banded case and the ...
Hugo J. Woerdeman, Mihály Bakonyi
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Semidefinite Programming in the Space of Partial Positive Semidefinite Matrices
SIAM Journal on Optimization, 2003Summary: 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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Positive Semidefinite Matrices
2018Positive semidefinite (PSD) and positive definite (PD) matrices are closely connected with Euclidean distance matrices. Accordingly, they play a central role in this monograph. This chapter reviews some of the basic results concerning these matrices.
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Graphs of Unitary Matrices and Positive Semidefinite Zero Forcing [PDF]
Reports on Mathematical Physics, 2013 The possible zero/nonzero patterns of unitary matrices are of interest in quantum evolution and the study of quantum systems on graphs. In particular, a quantum random walk can be defined on a directed graph if and only if that graph is associated with a
Brian Lins
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Positive Semidefinite Matrices
1999This 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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A new Farkas lemma for positive semidefinite matrices
IEEE Transactions on Automatic Control, 1995Let \(A\) be a linear mapping of the vector space of symmetric real matrices of a given size. Let \(S\) be a closed convex cone of positive matrices. The Farkas lemma characterizes the consistency of the system \(Ax= b\), \(x\in S\). The author obtains a variant that avoids the closeness assumption imposed on \(S+ \ker A\).
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Neural Computation, 2009
The correlation matrix is a fundamental statistic that used in many fields. For example, GroupLens, a collaborative filtering system, uses the correlation between users for predictive purposes. Since the correlation is a natural similarity measure between users, the correlation matrix may be used as the Gram matrix in kernel methods.
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The correlation matrix is a fundamental statistic that used in many fields. For example, GroupLens, a collaborative filtering system, uses the correlation between users for predictive purposes. Since the correlation is a natural similarity measure between users, the correlation matrix may be used as the Gram matrix in kernel methods.
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Inequalities on 2 × 2 block positive semidefinite matrices
Linear and Multilinear Algebra, 2022Pan-Shun Lau, Xiaohui Fu
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