•  
  •  
 

Keywords

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

Abstract

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)
Abstract

Included in

Algebra Commons

Share

COinS
 
 

To view the content in your browser, please download Adobe Reader or, alternately,
you may Download the file to your hard drive.

NOTE: The latest versions of Adobe Reader do not support viewing PDF files within Firefox on Mac OS and if you are using a modern (Intel) Mac, there is no official plugin for viewing PDF files within the browser window.