scholarly journals Trace inequalities for a block Hadamard product

Filomat ◽  
2018 ◽  
Vol 32 (1) ◽  
pp. 285-292
Author(s):  
Saliha Pehlivan ◽  
Mustafa Özel ◽  
Cenap Özel
Keyword(s):  
Kronecker Product ◽  
Hadamard Product ◽  
Type Inequality ◽  
Positive Semidefinite ◽  
Positive Semidefinite Matrices ◽  
Block Matrices ◽  
Trace Inequalities

In this paper, some inequalities for the trace and eigenvalues of a block Hadamard product of positive semidefinite matrices are investigated. In particular, a H?lder type inequality and inequalities related to norm and determinants of block matrices are obtained. Additionally, the relation between the trace of block Hadamard product and the usual Kronecker product is established.

scholarly journals TRACE INEQUALITIES FOR MATRICES

2012 ◽  
Vol 87 (1) ◽  
pp. 139-148 ◽  
Author(s):  
KHALID SHEBRAWI ◽  
HUSSIEN ALBADAWI
Keyword(s):  
Positive Integer ◽  
Positive Semidefinite ◽  
Positive Semidefinite Matrices ◽  
Image Position ◽  
The Given ◽  
Trace Inequalities ◽  
Products Of Matrices

AbstractTrace inequalities for sums and products of matrices are presented. Relations between the given inequalities and earlier results are discussed. Among other inequalities, it is shown that if A and B are positive semidefinite matrices then for any positive integer k.

scholarly journals A trace bound for integer-diagonal positive semidefinite matrices

2020 ◽  
Vol 8 (1) ◽  
pp. 14-16
Author(s):  
Lon Mitchell
Keyword(s):  
Positive Semidefinite ◽  
Positive Semidefinite Matrix ◽  
Positive Semidefinite Matrices ◽  
Semidefinite Matrix

AbstractWe prove that an n-by-n complex positive semidefinite matrix of rank r whose graph is connected, whose diagonal entries are integers, and whose non-zero off-diagonal entries have modulus at least one, has trace at least n + r − 1.

scholarly journals Fischer Type Log-Majorization of Singular Values on Partitioned Positive Semidefinite Matrices

2021 ◽  
Vol 2021 ◽  
pp. 1-5
Author(s):  
Benju Wang ◽  
Yun Zhang
Keyword(s):  
Singular Values ◽  
Positive Semidefinite ◽  
Positive Semidefinite Matrices ◽  
Fischer’S Inequality ◽  
New Inequalities

In this paper, we establish a Fischer type log-majorization of singular values on partitioned positive semidefinite matrices, which generalizes the classical Fischer's inequality. Meanwhile, some related and new inequalities are also obtained.

scholarly journals A Characterization of Polynomial Density on Curves via Matrix Algebra

Mathematics ◽  
2019 ◽  
Vol 7 (12) ◽  
pp. 1231
Author(s):  
Carmen Escribano ◽  
Raquel Gonzalo ◽  
Emilio Torrano
Keyword(s):  
Matrix Algebra ◽  
Optimization Problems ◽  
Positive Semidefinite ◽  
Point Of View ◽  
Alternative Proof ◽  
General Context ◽  
Positive Semidefinite Matrices ◽  
Jordan Curves ◽  
Point Evaluations

In this work, our aim is to obtain conditions to assure polynomial approximation in Hilbert spaces L 2 ( μ ) , with μ a compactly supported measure in the complex plane, in terms of properties of the associated moment matrix with the measure μ . To do it, in the more general context of Hermitian positive semidefinite matrices, we introduce two indexes, γ ( M ) and λ ( M ) , associated with different optimization problems concerning theses matrices. Our main result is a characterization of density of polynomials in the case of measures supported on Jordan curves with non-empty interior using the index γ and other specific index related to it. Moreover, we provide a new point of view of bounded point evaluations associated with a measure in terms of the index γ that will allow us to give an alternative proof of Thomson’s theorem, by using these matrix indexes. We point out that our techniques are based in matrix algebra tools in the framework of Hermitian positive definite matrices and in the computation of certain indexes related to some optimization problems for infinite matrices.

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