Convexity of the upper complex plane part of the numerical range of a quaternionic matrix

DOI10.1080/03081089608818484zbMath0876.15022OpenAlexW2086995396MaRDI QIDQ3123993

Robert C. Thompson, Wa-Sin So

Publication date: 23 November 1997

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

Full work available at URL: https://doi.org/10.1080/03081089608818484

zbMATH Keywords

quaternionic matrixelliptical range theoremquaternionic numerical rangealgebra of real quaternions

Mathematics Subject Classification ID

Matrices over special rings (quaternions, finite fields, etc.) (15B33) Norms of matrices, numerical range, applications of functional analysis to matrix theory (15A60)

Related Items (13)

Quaternionic Numerical Range and Real Subspaces ⋮ Numerical range of quaternionic right linear bounded operators ⋮ A note on convexity of sections of quaternionic numerical range ⋮ Boundary generating curves of quaternionic numerical ranges ⋮ The star-center of the quaternionic numerical range ⋮ The generalized numerical range of a set of matrices ⋮ On the boundedness of quaternionic numerical ranges with respect to nonstandard involutions ⋮ On the eigenvalues of quaternion matrices ⋮ The upper numerical range of a quaternionic matrix is not a complex numerical range ⋮ Quaternionic numerical range of complex matrices ⋮ A bridge between quaternionic and complex numerical ranges ⋮ S-spectrum and numerical range of a quaternionic operator ⋮ A new perspective on the quaternionic numerical range of normal matrices

Uses Software

• Mathematica

Cites Work

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• Matrices of quaternions
• On the convexity of numerical range in quaternionic hilbert spaces
• c-convex matrices: characterizations, inclusion relations and normality
• The numerical range of normal matrices with quaternion entries
• A short proof of a theorem on the numerical range of a normal quaternionic matrix
• Über den Wertevorrat einer Matrix

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