Classification of joint numerical ranges of three Hermitian matrices of size three
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Publication:1743079
DOI10.1016/j.laa.2017.11.017OpenAlexW2309751936WikidataQ112266747 ScholiaQ112266747MaRDI QIDQ1743079
Karol Życzkowski, Stephan Weis, Konrad Szymański
Publication date: 12 April 2018
Published in: Linear Algebra and its Applications (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1603.06569
Combinatorial properties of polytopes and polyhedra (number of faces, shortest paths, etc.) (52B05) Planar graphs; geometric and topological aspects of graph theory (05C10) Numerical range, numerical radius (47A12) Convex sets in (3) dimensions (including convex surfaces) (52A15) Convex sets in (n) dimensions (including convex hypersurfaces) (52A20) Convex sets and cones of operators (47L07)
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Cites Work
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- Numerical range for random matrices
- Semidefinite representation of convex hulls of rational varieties
- The numerical range of \(3 \times 3\) matrices
- Quantum convex support
- Sets of matrices with given joint numerical range
- Flat portions on the boundary of the Davis-Wielandt shell of 3-by-3 matrices
- Joint numerical range and its generating hypersurface
- Complementation in the face lattice of a proper cone
- Boundary generating curves of the \(c\)-numerical range
- A remark on the convexity and positive definiteness concerning Hermitian matrices
- Geometry of the numerical range of matrices
- Discriminant of the characteristic polynomial of a normal matrix
- Convexity of the joint numerical range: Topological and differential geometric viewpoints.
- 3 x 3 matrices with a flat portion on the boundary of the numerical range
- Joint numerical ranges, quantum maps, and joint numerical shadows
- Convexity of quadratic transformations and its use in control and optimization
- Real numerical shadow and generalized B-splines
- The lattice of faces of a finite dimensional cone
- Joint ranges of Hermitian matrices and simultaneous diagonalization
- Continuity of the maximum-entropy inference: Convex geometry and numerical ranges approach
- A Note on Touching Cones and Faces
- The possible shapes of numerical ranges
- Pre-images of boundary points of the numerical range
- Pre-images of extreme points of the numerical range, and applications
- Chapter 5: Dualities
- Semidefinite geometry of the numerical range
- Numerical shadow and geometry of quantum states
- Singular points of the ternary polynomials associated with 4-by-4 matrices
- Discriminant of symmetric matrices as a sum of squares and the orthogonal group
- Geometry of the generalized Bloch sphere for qutrits
- The joint essential numerical range, compact perturbations, and the Olsen problem
- Nondifferentiabie points of ∂Wc(A)
- On the crossing rule
- A simple proof of the elliptical range theorem
- Geometry of the Set of Mixed Quantum States: An Apophatic Approach
- Dissecting the qutrit
- Convexity of the Joint Numerical Range
- Discontinuity of maximum entropy inference and quantum phase transitions
- Generating random density matrices
- Geometry of Quantum States
- Multiplicities, boundary points, and {joint} numerical ranges
- Convex Bodies The Brunn-MinkowskiTheory
- SOLUTION OF THE HEAWOOD MAP-COLORING PROBLEM
- 3-by-3 matrices with elliptical numerical range revisited
- Über den Wertevorrat einer Matrix
- Symmetry breaking and the geometry of reduced density matrices
- Geometry of Bloch vectors in two-qubit system