Geometry of higher-rank numerical ranges

DOI10.1080/03081080701336545zbMath1137.15016OpenAlexW2096331293MaRDI QIDQ5443474

Man-Duen Choi, David W. Kribs, Michael Giesinger, John A. R. Holbrook

Publication date: 21 February 2008

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

Full work available at URL: https://doi.org/10.1080/03081080701336545

zbMATH Keywords

convexityhigher rank numerical rangeToeplitz-Hausdorff theorem

Mathematics Subject Classification ID

Norms of matrices, numerical range, applications of functional analysis to matrix theory (15A60)

Related Items (28)

Linear preservers of higher rank numerical ranges and radii ⋮ Joint higher rank numerical range of Pauli group ⋮ Factorization of Singular Matrix Polynomials and Matrices with Circular Higher Rank Numerical Ranges ⋮ Higher-rank numerical ranges and Kippenhahn polynomials ⋮ Partial isospectrality of a matrix pencil and circularity of the \(c\)-numerical range ⋮ Numerical shadows: measures and densities on the numerical range ⋮ Shell extremal eigenvalues of tridiagonal Toeplitz Matrices ⋮ Canonical forms, higher rank numerical ranges, totally isotropic subspaces, and matrix equations ⋮ Higher rank numerical ranges of normal operators and unitary dilations ⋮ Unnamed Item ⋮ Isospectrality and matrices with concentric circular higher rank numerical ranges ⋮ Higher rank numerical ranges and low rank perturbations of quantum channels ⋮ Elliptical higher rank numerical range of some Toeplitz matrices ⋮ Entropy of a Quantum Error Correction Code ⋮ The mathematics of Chandler Davis ⋮ Real higher rank numerical ranges and ellipsoids ⋮ Multiplicative maps preserving the higher rank numerical ranges and radii ⋮ Product of operators and numerical range ⋮ Protected subspaces in quantum information ⋮ Generalized numerical ranges, dilation, and quantum error correction ⋮ Condition for the higher rank numerical range to be non-empty ⋮ An Inverse Problem for the $k$-Rank Numerical Range ⋮ Private quantum codes: introduction and connection with higher rank numerical ranges ⋮ Unnamed Item ⋮ Higher rank matricial ranges and hybrid quantum error correction ⋮ Bounds on polygons of higher rank numerical ranges ⋮ Isoclinic subspaces and quantum error correction ⋮ Generalized interlacing inequalities

Cites Work

• Higher-rank numerical ranges and compression problems
• Quantum error correcting codes from the compression formalism
• On thekth matrix numerical range
• Matrical extensions of the numerical range: a brief survey

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