\(\mathbb G\)-reflectors: Analogues of Householder transformations in scalar product spaces

DOI10.1016/j.laa.2003.07.009zbMath1059.65040OpenAlexW2110773940MaRDI QIDQ1827506

Françoise Tisseur, Niloufer Mackey, D. Steven Mackey

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.2003.07.009

zbMATH Keywords

algorithmsymmetriesbilinear formscalar productstructure-preserving algorithmHouseholder transformationssymplecticisotropicsesquilinear formtransvectionsreflectororthosymmetrichyperbolic transformationpseudo-unitary

Mathematics Subject Classification ID

Related Items (18)

Generalized elliptical quaternions with some applications ⋮ An alternative approach to elliptical motion ⋮ Structure-preserving diagonalization of matrices in indefinite inner product spaces ⋮ One Parameter Elliptic Motions in Three-Dimensional Space ⋮ Unnamed Item ⋮ On elliptical motions on a general ellipsoid ⋮ An algorithm for the Cartan-Dieudonné theorem on generalized scalar product spaces ⋮ A constructive proof of the Cartan-Dieudonné-Scherk theorem in the real or complex case ⋮ The \(\Lambda _{S}\)-Householder matrices ⋮ Optimal symplectic Householder transformations for \(SR\) decomposition ⋮ Orthosymmetric block reflectors ⋮ A structure-preserving \(QR\) factorization for centrosymmetric real matrices ⋮ The Cartan-Dieudonné-Scherk theorems for complex \(S\)-orthogonal matrices ⋮ Fast direct solvers for some complex symmetric block Toeplitz linear systems ⋮ On theoretical and numerical aspects of symplectic Gram-Schmidt-like algorithms ⋮ Generating hyperbolical rotation matrix for a given hyperboloid ⋮ Non-parabolic conical rotations ⋮ \(S\) orthogonal matrices and \(S\) symmetries

Uses Software

• LAPACK
• NAG
• mctoolbox
• nag
• CLARFG

Cites Work

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• Matrices and indefinite scalar products
• Schur-like forms for matrix Lie groups, Lie algebras and Jordan algebras
• Unifying unitary and hyperbolic transformations
• Structured Mapping Problems for Matrices Associated with Scalar Products. Part I: Lie and Jordan Algebras
• Hyperbolic householder transformations
• LAPACK Users' Guide
• On Hyperbolic Triangularization: Stability and Pivoting
• The computation of elementary unitary matrices
• Structured tools for structured matrices
• Accuracy and Stability of Numerical Algorithms
• On computing givens rotations reliably and efficiently
• Structured Factorizations in Scalar Product Spaces
• On the Decomposition of Orthogonalities into Symmetries
• Constructive ways for generating (generalized) real orthogonal matrices as products of (generalized) symmetries

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