Results 21 to 30 of about 597 (98)
Some generalizations and complements of determinantal inequalities
, 2020 K. Audenaert in [1] formulated a determinantal inequality arising from diffusion tensor imaging. Very recently M. Lin proved in [6] a complement and proposed a conjecture.
H. Abbas, Mohammad M. Ghabries
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Matrix Ostrowski inequality via the matrix geometric mean
Journal of Mathematical Inequalities, 2020 In this paper, we show a symmetric generalization of the Ostrowski inequality due to Fujii, Lin and Nakamoto. Moreover, we show its two variable extenstion.
Ryosuke Nakayama, Y. Seo, Reo Tojo
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Singular value inequalities for matrices with numerical ranges in a sector
, 2014 Let A = [ A11 A12 A21 A22 ] , where A22 is q× q , be an n× n complex matrix such that the numerical range of A is contained in Sα = {z ∈ C : Rz > 0, |Iz| (Rz) tanα} for some α ∈ [0,π/2) . We obtain the following singular value inequality: σ j(A/A11) sec2(
S. Drury, Minghua Lin
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Inequalities for the λ-weighted mixed arithmetic-geometric-harmonic means of sector matrices
, 2020 In this note, we first explain a minor error in the literature [3]. Secondly, we prove the λ -weighted mixed arithmetic-geometric-harmonic-mean inequalities of A and B which are the generalizations of the results already introduced in [3].
Song Lin, Xiaohui Fu
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A note on a conjectured singular value inequality related to a linear map
, 2020 If ( A D D∗ C ) is positive semidefinite with each block n×n, Lin conjectured that s j(Φ(D)) s j(Φ(A) Φ(C)), j = 1, . . . ,n, where Φ is the linear map: D → D+(trD)In and s j(D) denotes the j -th largest singular value of the matrix D .
Junj an Yang, Lin Lu, Zhen Chen
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THE GROTHENDIECK CONSTANT IS STRICTLY SMALLER THAN KRIVINE’S BOUND
Forum of Mathematics, Pi, 2013 The (real) Grothendieck constant ${K}_{G} $ is the infimum over those $K\in (0, \infty )$ such that for every $m, n\in \mathbb{N} $ and every $m\times n$ real matrix $({a}_{ij} )$ we have $$\begin{eqnarray*}\displaystyle \max _{\{ x_{i}\} _{i= 1}^{m} , \{
MARK BRAVERMAN +3 more
doaj +1 more source
An extension of Hartfiel's determinant inequality
, 2018 Let A and B be n× n positive definite matrices, Hartfiel obtained a lower bound for det(A + B) . In this paper, we first extend his result to det(A + B +C) , where A,B and C are n× n positive definite matrices, and then show a generalization of this to ...
L. Hou, S. Dong
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Vector-Valued Maclaurin Inequalities [PDF]
arXiv, 2021 We investigate a Maclaurin inequality for vectors and its connection to an Aleksandrov-type inequality for parallelepipeds.
arxiv
A survey on the Böttcher-Wenzel conjecture and related problems
, 2015 A fundamental fact in matrix theory is that the matrix multiplication is not commutative, i.e., there are square matrices X and Y such that XY = YX . The difference XY −YX is called the commutator (or Lie product) of X and Y .
Chen Cheng, Xiao-Qing Jin, Seakweng Vong
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Schr\"odinger uncertainty relation, Wigner-Yanase-Dyson skew information and metric adjusted correlation measure [PDF]
, 2012 In this paper, we give a Schr\"odinger-type uncertainty relation using the Wigner-Yanase-Dyson skew information. In addition, we give Schr\"odinger-type uncertainty relation by use of a two-parameter extended correlation measure.
Audenaert +38 more
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