Structured Factorizations in Scalar Product Spaces

DOI10.1137/040619363zbMath1098.15005OpenAlexW2104914078WikidataQ114074397 ScholiaQ114074397MaRDI QIDQ5470496

D. Steven Mackey, Françoise Tisseur, Niloufer Mackey

Publication date: 31 May 2006

Published in: SIAM Journal on Matrix Analysis and Applications (Search for Journal in Brave)

Full work available at URL: http://eprints.maths.manchester.ac.uk/976/1/Tisseur.pdf

zbMATH Keywords

automorphism groupeigenvaluesHamiltonianeigenvectorsindefinite inner productLie algebraLie groupmatrix square rootfactorizationsingular valuesbilinear formadjointpolar decompositionJordan algebrascalar productmatrix sign functiongeneralized polar decompositionsymplecticsesquilinear formstructure preservationorthosymmetricpseudo-orthogonal

Mathematics Subject Classification ID

Factorization of matrices (15A23) Quadratic and bilinear forms, inner products (15A63)

Related Items (40)

Linearizations of matrix polynomials in Bernstein bases ⋮ Structure-preserving diagonalization of matrices in indefinite inner product spaces ⋮ A Kogbetliantz-type algorithm for the hyperbolic SVD ⋮ Some remarks on the complex \(J\)-symmetric eigenproblem ⋮ Finite-Dimensional Indefinite Inner Product Spaces and Applications in Numerical Analysis ⋮ Symplectic analogs of polar decomposition and their applications to bosonic Gaussian channels ⋮ Linearizations of matrix polynomials in Newton bases ⋮ A unitary similarity transform of a normal matrix to complex symmetric form ⋮ Stable and Efficient Computation of Generalized Polar Decompositions ⋮ Skew-symmetric matrix polynomials and their Smith forms ⋮ Singular value decomposition for skew-Takagi factorization with quantum applications ⋮ A Structure-Preserving Divide-and-Conquer Method for Pseudosymmetric Matrices ⋮ Fifty Three Matrix Factorizations: A Systematic Approach ⋮ Structure preserving parallel algorithms for solving the Bethe-Salpeter eigenvalue problem ⋮ Unnamed Item ⋮ On a reverse Heinz-Kato-Furuta inequality ⋮ The hyperbolic Schur decomposition ⋮ Symmetric spaces and Lie triple systems in numerical analysis of differential equations ⋮ \(m\) th roots of \(H\)-selfadjoint matrices ⋮ Efficient and accurate algorithms for solving the Bethe-Salpeter eigenvalue problem for crystalline systems ⋮ A structure-preserving \(QR\) factorization for centrosymmetric real matrices ⋮ Preserving spectral properties of structured matrices under structured perturbations ⋮ A Padé family of iterations for the matrix sector function and the matrix p th root ⋮ The coninvolutory decomposition and its computation for a complex matrix ⋮ On tridiagonal matrices unitarily equivalent to normal matrices ⋮ Symplectic Lattice Reduction and NTRU ⋮ Simple forms for perplectic and symplectic normal matrices ⋮ Approximation of matrices and a family of Gander methods for polar decomposition ⋮ A new polar decomposition in a scalar product space ⋮ Factorizations into normal matrices in indefinite inner product spaces ⋮ On the diagonalizability of a matrix by a symplectic equivalence, similarity or congruence transformation ⋮ A spectral trichotomy method for symplectic matrices ⋮ Products of positive definite symplectic matrices ⋮ Doppler shift in semi-Riemannian signature and the non-uniqueness of the Krein space of spinors ⋮ 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 ⋮ \(\mathbb G\)-reflectors: Analogues of Householder transformations in scalar product spaces ⋮ Non-parabolic conical rotations ⋮ On the structure of the solutions to the matrix equation \(G^\ast JG = J\) ⋮ Polynomial-time algorithms for quadratic isomorphism of polynomials: the regular case

This page was built for publication: Structured Factorizations in Scalar Product Spaces