An Extension of the Hausdorff-Toeplitz Theorem on the Numerical Range
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Publication:3039952
DOI10.2307/2044904zbMath0525.47002OpenAlexW4247435679MaRDI QIDQ3039952
Yik-Hoi Au-Yeung, Nam-Kiu Tsing
Publication date: 1983
Full work available at URL: https://doi.org/10.2307/2044904
Norms of matrices, numerical range, applications of functional analysis to matrix theory (15A60) Numerical range, numerical radius (47A12)
Related Items (34)
H-joint numerical ranges ⋮ On the joint numerical radius parallelism of operators ⋮ Joint k-numerical ranges of operators ⋮ Convexity of generalized numerical range associated with a compact Lie group ⋮ Polynomials and Numerical Ranges ⋮ On minimizing the largest eigenvalue of a symmetric matrix ⋮ On Birkhoff-James and Roberts orthogonality ⋮ Reduction of joint \(c\)-numerical ranges ⋮ A distance formula for tuples of operators ⋮ Joint ranges of Hermitian matrices and simultaneous diagonalization ⋮ Complete controllability and contractibility in multimodal systems ⋮ The inverse \(q\)-numerical range problem and connections to the Davis-Wielandt shell and the pseudospectra of a matrix ⋮ Convexity and star-shapedness of matricial range ⋮ Strict convexity of the joint \(c\)-numerical range ⋮ Reduction of the \(c\)-numerical range to the classical numerical range ⋮ Davis-Wielandt radius inequalities for off-diagonal operator matrices ⋮ Roberts orthogonality and Davis-Wielandt shell ⋮ Joint numerical ranges and commutativity of matrices ⋮ Variational Characterization of Monotone Nonlinear Eigenvector Problems and Geometry of Self-Consistent Field Iteration ⋮ On generalized numerical range of the Aluthge transformation. ⋮ Toeplitz matrices are unitarily similar to symmetric matrices ⋮ Generalized numerical ranges, joint positive definiteness and multiple eigenvalues ⋮ The generalized numerical range of a set of matrices ⋮ Convexity of quadratic transformations and its use in control and optimization ⋮ The normalized numerical range and the Davis-Wielandt shell ⋮ Remarks on numerical ranges of operators in spaces with an indefinite metric ⋮ Flat portions on the boundary of the Davis-Wielandt shell of 3-by-3 matrices ⋮ Computing the numerical range of Krein space operators ⋮ The star-shapedness of a generalized numerical range ⋮ Joint zero sets and ranges of several Hermitian forms over complex and quaternionic scalars ⋮ Joint numerical range and its generating hypersurface ⋮ Numerical range of linear pencils ⋮ Matrix pencils with the numerical range equal to the whole complex plane ⋮ Definite triples of Hermitian matrices and matrix polynomials
Cites Work
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- A remark on the convexity and positive definiteness concerning Hermitian matrices
- Subspaces of symmetric matrices containing matrices with a multiple first eigenvalue
- Elementary inclusion relations for generalized numerical ranges
- Über das Vorkommen definiter und semidefiniter Formen in Scharen quadratischer Formen
- Some theorems on the generalized numerical ranges
- Another proof of a result of Westwick
- A theorem on numerical range
- Linear Systems of Real Quadratic Forms
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