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- W2010188279 abstract "Gustafson, Halmos, and Radjavi in 1973 proved that each matrix A with det A = ± 1 is a product of four involutions. We prove that these involutions can be taken to be symplectic if A is symplectic (every symplectic matrix has unit determinant). Using this result we give an alternative proof of Laffey's theorem that every nonsingular even size matrix is a product of skew symmetric matrices. Ballantine in 1978 proved that each matrix A with | det A | = 1 is a product of four coninvolutions. We prove that these coninvolutions can be taken to be symplectic if A is symplectic. We also prove that each Hamiltonian matrix is a sum of two square zero Hamiltonian matrices." @default.
- W2010188279 created "2016-06-24" @default.
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- W2010188279 date "2015-02-01" @default.
- W2010188279 modified "2023-10-17" @default.
- W2010188279 title "Each symplectic matrix is a product of four symplectic involutions" @default.
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- W2010188279 doi "https://doi.org/10.1016/j.laa.2014.10.016" @default.
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