Symplectic matrices, Product of unipotent matrices, Symplectic Jordan Canonical Form


In this article, it is proved that every symplectic matrix can be decomposed into a product of three symplectic unipotent matrices of index 2, i.e., every complex matrix $A$ satisfying $A^{T}JA=J$ with $J =\begin{bmatrix} 0 & I_{n} \\ -I_{n} & 0 \end{bmatrix}$ is a product of three matrices $B_{i}$ satisfying $B_{i}^{T}JB_{i}=J$ and $(B_{i}-I)^2=0$ $(i=1,2,3)$.

abs_vol35_pp497-502.pdf (138 kB)

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