Each symplectic matrix is a product of four symplectic involutions

DOI10.1016/j.laa.2014.10.016zbMath1310.15020OpenAlexW2010188279MaRDI QIDQ472445

Ralph John de la Cruz

Publication date: 19 November 2014

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

Full work available at URL: https://doi.org/10.1016/j.laa.2014.10.016

zbMATH Keywords

involutionsHamiltonian matricessymplectic matricesconinvolutionssquare zero matrices

Mathematics Subject Classification ID

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

Related Items (19)

Products of commutators of symplectic involutions ⋮ Unnamed Item ⋮ Every real symplectic matrix is a product of real symplectic involutions ⋮ Generation of the symplectic group by involutions ⋮ Reality of unipotent elements in classical Lie groups ⋮ Products of two involutions in orthogonal and symplectic groups ⋮ The sums of symplectic, Hamiltonian, and skew-Hamiltonian matrices ⋮ Products of symplectic normal matrices ⋮ The quadratic sum problem for symplectic pairs ⋮ Decomposition of symplectic matrices into products of commutators of symplectic involutions ⋮ Unnamed Item ⋮ The subspaces spanned by Householder vectors associated with an orthogonal or a symplectic matrix ⋮ Each \(2n\)-by-\(2n\) complex symplectic matrix is a product of \(n+1\) commutators of \(J\)-symmetries ⋮ Every \(2n\)-by-\(2n\) complex matrix is a sum of three symplectic matrices ⋮ On the diagonalizability of a matrix by a symplectic equivalence, similarity or congruence transformation ⋮ Products of positive definite symplectic matrices ⋮ 2n-by-2n symplectic completions of matrices of order 2n − 1 ⋮ Products of Riordan arrays of finite orders ⋮ Every real symplectic matrix is a product of commutators of real symplectic involutions

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