Information geometry of operator scaling

DOI10.1016/j.laa.2022.04.022OpenAlexW3021578357WikidataQ114151574 ScholiaQ114151574MaRDI QIDQ2151570

Takeru Matsuda, Tasuku Soma

Publication date: 5 July 2022

Published in: Linear Algebra and its Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2005.01453

zbMATH Keywords

information geometrycompletely positive mapsymmetric logarithmic derivativeoperator scalingSinkhorn algorithm

Mathematics Subject Classification ID

Norms of matrices, numerical range, applications of functional analysis to matrix theory (15A60) Quantum information, communication, networks (quantum-theoretic aspects) (81P45) Differential geometric aspects of statistical manifolds and information geometry (53B12)

Related Items (1)

Non-negative low-rank approximations for multi-dimensional arrays on statistical manifold

Cites Work

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• Information geometry and its applications
• Riemannian metrics on positive definite matrices related to means
• I-divergence geometry of probability distributions and minimization problems
• Completely positive linear maps on complex matrices
• Constructive non-commutative rank computation is in deterministic polynomial time
• On variational expressions for quantum relative entropies
• Semidefinite approximations of the matrix logarithm
• Algorithmic and optimization aspects of Brascamp-Lieb inequalities, via operator scaling
• Classical complexity and quantum entanglement
• Monotone metrics on matrix spaces
• Operator scaling: theory and applications
• The Bogoliubov inner product in quantum statistics
• Non-commutative Edmonds' problem and matrix semi-invariants
• Quantum information theory and quantum statistics.
• Dualistic differential geometry of positive definite matrices and its applications to related problems
• Positive Definite Matrices
• Matrix Nearness Problems with Bregman Divergences
• Nonnegative Matrix Factorization with the Itakura-Saito Divergence: With Application to Music Analysis
• Two quantum analogues of Fisher information from a large deviation viewpoint of quantum estimation
• Statistical Manifolds Admitting Torsion and Partially Flat Spaces
• Editorial IMA IAI - Information and Inference special issue on optimal transport in data sciences
• Operator scaling via geodesically convex optimization, invariant theory and polynomial identity testing
• Operator scaling with specified marginals
• Data assimilation: The Schrödinger perspective
• Positive contraction mappings for classical and quantum Schrödinger systems
• A Relationship Between Arbitrary Positive Matrices and Doubly Stochastic Matrices
• Conditional expectation in an operator algebra. IV. Entropy and information
• Introduction to matrix analysis and applications

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