Inequalities related to 2 ✕ 2 block PPT matrices

DOI10.7153/oam-09-54zbMath1345.15004OpenAlexW2514525871MaRDI QIDQ2814829

Minghua Lin

Publication date: 23 June 2016

Published in: Operators and Matrices (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.7153/oam-09-54

zbMATH Keywords

traceinequalitysingular valuepositive partial transpose matrix

Mathematics Subject Classification ID

Determinants, permanents, traces, other special matrix functions (15A15) Inequalities involving eigenvalues and eigenvectors (15A42) Norms of matrices, numerical range, applications of functional analysis to matrix theory (15A60) Miscellaneous inequalities involving matrices (15A45) Channel models (including quantum) in information and communication theory (94A40) Quantum information, communication, networks (quantum-theoretic aspects) (81P45)

Related Items (30)

Refining some inequalities on 2 × 2 block accretive matrices ⋮ Inequalities on 2 × 2 block positive semidefinite matrices ⋮ Unnamed Item ⋮ More results related to geometric mean and singular values for matrices ⋮ The Hua matrix and inequalities related to contractive matrices ⋮ A new matrix inequality involving partial traces ⋮ Some singular value inequalities related to linear maps ⋮ Some applications of two completely copositive maps ⋮ Remarks on two recent results of Audenaert ⋮ Improvements on some partial trace inequalities for positive semidefinite block matrices ⋮ Trace inequalities related to 2 × 2 block sector matrices ⋮ On 2×2 positive matrices of τ-measurable operators ⋮ A generalized Hölder type eigenvalue inequality ⋮ Submajorization and p-norm inequalities associated with -measurable operators ⋮ On submajorization inequalities for matrices of measurable operators ⋮ Linear maps of positive partial transpose matrices and singular value inequalities ⋮ Inequalities related to partial trace and block Hadamard product ⋮ The off-diagonal block of a PPT matrix ⋮ New properties for certain positive semidefinite matrices ⋮ Unnamed Item ⋮ Trace inequalities for positive semidefinite block matrices ⋮ On some inequalities related to positive block matrices ⋮ Some new results for Hua-type operator matrices ⋮ Notes on two recent results of Audenaert ⋮ Geometry and inequalities of geometric mean ⋮ Some inequalities related to \(2\times 2\) block sector partial transpose matrices ⋮ A note on a conjectured singular value inequality related to a linear map ⋮ Extensions of some matrix inequalities related to trace and partial traces ⋮ Inequalities related to the geometric mean of accretive matrices ⋮ Trace inequalities involving positive semi-definite block matrices

Cites Work

• Norm inequalities related to the matrix geometric mean
• Separability of mixed states: necessary and sufficient conditions.
• Norm inequalities for accretive-dissipative operator matrices
• Positivity of operator-matrices of Hua-type
• The matrix arithmetic-geometric mean inequality revisited
• Hiroshima’s theorem and matrix norm inequalities
• Contractive matrices of Hua type
• Separability Criterion for Density Matrices

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