Several observations on symplectic, Hamiltonian, and skew-Hamiltonian matrices

DOI10.1016/j.laa.2004.12.012zbMath1077.15010OpenAlexW2073979097MaRDI QIDQ1779250

Khakim D. Ikramov, Heike Fassbender

Publication date: 1 June 2005

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

Full work available at URL: https://doi.org/10.1016/j.laa.2004.12.012

zbMATH Keywords

singular value decompositioncondition numberfactorizationHamiltonian matrixsymplectic matrixsimilarity transformationspencils of matricesstrict equivalence\(J\)-Hermitian matrix\(T\)-congruencedefinite Hermitian pair\(J\)-skew-Hermitian matrixconjugate symplectic matrixskew Hamiltonian matrix

Mathematics Subject Classification ID

Factorization of matrices (15A23) Hermitian, skew-Hermitian, and related matrices (15B57) Canonical forms, reductions, classification (15A21) Conditioning of matrices (15A12) Matrix pencils (15A22)

Related Items (7)

Symmetric Fermi projections and Kitaev’s table: Topological phases of matter in low dimensions ⋮ Diagonalizability with respect to perplectic and pseudo-unitary similarity transformations ⋮ Fifty Three Matrix Factorizations: A Systematic Approach ⋮ Algebraic vs physical N = 6 3-algebras ⋮ Similarity vs unitary similarity and perturbation analysis of sign characteristics: complex and real indefinite inner products ⋮ When is a Hamiltonian matrix the commutator of two skew-Hamiltonian matrices? ⋮ The Structured Condition Number of a Differentiable Map between Matrix Manifolds, with Applications

Cites Work

• Unnamed Item
• A Jacobi eigenreduction algorithm for definite matrix pairs
• An SVD-like matrix decomposition and its applications
• Matrix Analysis
• Computing the Polar Decomposition and the Matrix Sign Decomposition in Matrix Groups
• Structured tools for structured matrices

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