Inequalities on 2 × 2 block positive semidefinite matrices

Fu, Xiaohui; Lau, Pan-Shun; Tam, Tin-Yau

doi:10.1080/03081087.2021.1969327

Cited by 5 publications

(2 citation statements)

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“…It is worth noting that the 2-copositivity of Ψ could also lead to the previous (14); see [23] for more details. Another attractive application of Theorem 4.1 states that if A ∈ M m (M n ) is positive semidefinite, by using the 2-copositivity of Ψ(X) = (trX)I − X, one can obtain Ando's result (3).…”

Section: Inequalities About Two Partial Tracesmentioning

confidence: 99%

“…If both A and A τ are positive semidefinite, then A is said to be positive partial transpose (or PPT for short). For more explanations and applications of the PPT matrices, we recommend a comprehensive monograph [6], and see, e.g., [27,20,41,14] for recent results. Next we introduce the definition of two partial traces tr 1 A and tr 2 A of A.…”

Section: Introductionmentioning

confidence: 99%

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Improvements on some partial trace inequalities for positive semidefinite block matrices

2021

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We study matrix inequalities involving partial traces for positive semidefinite block matrices. First of all, we present a new method to prove a celebrated result of Choi [Linear Algebra Appl. 516 (2017)]. Our method also allows us to prove a generalization of another result of Choi [Linear Multilinear Algebra 66 (2018)]. Furthermore, we shall give an improvement on a recent result of Li, Liu and Huang [Operators and Matrices 15 (2021)]. In addition, we include with some majorization inequalities involving partial traces for two by two block matrices, and also provide inequalities related to the unitarily invariant norms as well as the singular values, which can be viewed as slight extensions of two results of Lin [Linear Algebra Appl. 459 (2014)] and [Electronic J. Linear Algebra 31 (2016)].

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Section: Inequalities About Two Partial Tracesmentioning

confidence: 99%