On symplectic eigenvalues of positive definite matrices

DOI10.1063/1.4935852zbMath1329.15048arXiv1803.04647OpenAlexW3100659610MaRDI QIDQ3457157

Tanvi Jain, Rajendra Bhatia

Publication date: 10 December 2015

Published in: Journal of Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1803.04647

zbMATH Keywords

variational principlesinequalities involving eigenvaluespositive definite matrixsymplectic matrixperturbation theoremsymplectic eigenvaluesRiemannian mean

Mathematics Subject Classification ID

Inequalities involving eigenvalues and eigenvectors (15A42) Positive matrices and their generalizations; cones of matrices (15B48)

Related Items (24)

Log-majorizations for the (symplectic) eigenvalues of the Cartan barycenter ⋮ Perturbation bounds for Williamson's symplectic normal form ⋮ Derivatives of symplectic eigenvalues and a Lidskii type theorem ⋮ Complexity of mixed Gaussian states from Fisher information geometry ⋮ Diagonalizability with respect to perplectic and pseudo-unitary similarity transformations ⋮ A Schur-Horn theorem for symplectic eigenvalues ⋮ Symplectic spaces and pairs of symmetric and nonsingular skew-symmetric matrices under congruence ⋮ A note on ``Perturbation bounds for Williamson's symplectic normal form ⋮ Fifty Three Matrix Factorizations: A Systematic Approach ⋮ A new version of Schur–Horn type theorem ⋮ Entanglement structure of quantum fields through local probes ⋮ First order sensitivity analysis of symplectic eigenvalues ⋮ New properties of a special matrix related to positive-definite matrices ⋮ Symplectic eigenvalues of positive-semidefinite matrices and the trace minimization theorem ⋮ Subsystem complexity after a local quantum quench ⋮ Variational principles for symplectic eigenvalues ⋮ Sums and products of symplectic eigenvalues ⋮ A Szegő type theorem and distribution of symplectic eigenvalues ⋮ Some inequalities for eigenvalues and symplectic eigenvalues of positive definite matrices ⋮ Riemannian Optimization on the Symplectic Stiefel Manifold ⋮ Rajendra Bhatia and his mathematical achievements ⋮ On generalizing trace minimization principles ⋮ Computing Symplectic Eigenpairs of Symmetric Positive-Definite Matrices via Trace Minimization and Riemannian Optimization ⋮ Geometry of the symplectic Stiefel manifold endowed with the Euclidean metric

Cites Work

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• Monotonicity of the matrix geometric mean
• Monotonic properties of the least squares mean
• Gaussian quantum marginal problem
• Functional calculus for sesquilinear forms and the purification map
• Singular values, doubly stochastic matrices, and applications
• Positive definite matrices
• Symplectic geometry and quantum mechanics
• The Symmetry Group of Gaussian States in $${L}^{2}({\mathbb{R}}^{n})$$
• Inequalities for quantum marginal problems with continuous variables
• The Riemannian Mean of Positive Matrices
• Weighted deterministic walks for the least squares mean on Hadamard spaces
• Inequalities: theory of majorization and its applications

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