The subspaces spanned by Householder vectors associated with an orthogonal or a symplectic matrix

DOI10.1016/j.laa.2018.02.002zbMath1390.15037OpenAlexW2792875405MaRDI QIDQ1743130

Agnes T. Paras, Dennis I. Merino, Kennett L. de la Rosa

Publication date: 12 April 2018

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

Full work available at URL: https://doi.org/10.1016/j.laa.2018.02.002

zbMATH Keywords

symplectic matricesorthogonal matrices\(S\)-orthogonal matrices\(S\)-symmetry

Mathematics Subject Classification ID

Factorization of matrices (15A23) Canonical forms, reductions, classification (15A21)

Related Items

Every real symplectic matrix is a product of real symplectic involutions

Cites Work

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• Each symplectic matrix is a product of four symplectic involutions
• Each \(2n\)-by-\(2n\) complex symplectic matrix is a product of \(n+1\) commutators of \(J\)-symmetries
• The Jordan canonical forms of complex orthogonal and skew-symmetric matrices
• The Cartan-Dieudonné-Scherk theorems for complex \(S\)-orthogonal matrices
• \(S\) orthogonal matrices and \(S\) symmetries
• The QR algorithm: 50 years later its genesis by John Francis and Vera Kublanovskaya and subsequent developments
• On the Decomposition of Orthogonalities into Symmetries