Companion matrices: Reducibility, numerical ranges and similarity to contractions

DOI10.1016/j.laa.2003.11.027zbMath1063.15025OpenAlexW1996970467MaRDI QIDQ1826841

Pei Yuan Wu, Hwa-Long Gau

Publication date: 6 August 2004

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

Full work available at URL: https://doi.org/10.1016/j.laa.2003.11.027

zbMATH Keywords

contractionnumerical rangecompanion matrixdefect indexreducible matrixunitary-equivalence

Mathematics Subject Classification ID

Norms of matrices, numerical range, applications of functional analysis to matrix theory (15A60) Canonical forms, reductions, classification (15A21)

Related Items (19)

Numerical radii for tensor products of matrices ⋮ Numerical ranges of reducible companion matrices ⋮ Numerical ranges of companion matrices ⋮ Determinantal representations of invariant hyperbolic plane curves ⋮ Weighted shift matrices: unitary equivalence, reducibility and numerical ranges ⋮ Crawford numbers of companion matrices ⋮ Higher-rank numerical ranges and Kippenhahn polynomials ⋮ Flat portions of the numerical range of a \(6 \times 6\) companion matrix ⋮ Unnamed Item ⋮ Elliptic numerical ranges of \(3 \times 3\) companion matrices ⋮ Numerical ranges of nilpotent operators ⋮ Uniqueness problem on numerical ranges of 3-by-3 companion matrices ⋮ The numerical range of a periodic tridiagonal operator reduces to the numerical range of a finite matrix ⋮ Flat portions on the boundary of the numerical ranges of certain Toeplitz matrices ⋮ On the Block Numerical Range of Nonnegative Matrices ⋮ Zero-dilation Index of S_n-matrix and Companion Matrix ⋮ Equality of numerical ranges of matrix powers ⋮ Kippenhahn's Theorem for Joint Numerical Ranges and Quantum States ⋮ Numerical ranges of companion matrices: flat portions on the boundary

Cites Work

• The numerical range of \(3 \times 3\) matrices
• The Numerical Radius of a Nilpotent Operator on a Hilbert Space
• Analytic Programmes in Matrix Algebras
• Explicit polar decomposition of companion matrices
• Über den Wertevorrat einer Matrix
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item

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