Structure-preserving diagonalization of matrices in indefinite inner product spaces

zbMath1435.15027arXiv1910.12307MaRDI QIDQ5217410

Philip Saltenberger

Publication date: 27 February 2020

Full work available at URL: https://arxiv.org/abs/1910.12307

zbMATH Keywords

symplectic matricesdiagonalizationunitary matricessesquilinear formsLagrangian subspaces(skew)-Hamiltonian matricesper(skew)-Hermitian matricesperplectic matrices

Mathematics Subject Classification ID

Factorization of matrices (15A23) Hermitian, skew-Hermitian, and related matrices (15B57) Bilinear and Hermitian forms (11E39) Quadratic and bilinear forms, inner products (15A63)

Related Items (1)

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Cites Work

• A Schur decomposition for Hamiltonian matrices
• Normal matrices
• \(\mathbb G\)-reflectors: Analogues of Householder transformations in scalar product spaces
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• The Quadratic Eigenvalue Problem
• Existence, Uniqueness, and Parametrization of Lagrangian Invariant Subspaces
• Breaking Van Loan’s Curse: A Quest forStructure-Preserving Algorithms for Dense Structured Eigenvalue Problems
• The Elements of Operator Theory
• A Chart of Numerical Methods for Structured Eigenvalue Problems
• Structured Jordan canonical forms for structured matrices that are hermitian, skew hermitian or unitary with respect to indefinite inner products
• Structure preserving algorithms for perplectic eigenproblems
• Continuous Lattices and Domains
• Naive Lie Theory
• Functions of Matrices
• Structured Factorizations in Scalar Product Spaces
• On the diagonalizability of a matrix by a symplectic equivalence, similarity or congruence transformation
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