05. Symplectic Matrix

A transformation matrix T with an even number of rows and columns is called symplectic iff .

(with being the transposed matrix T)

(with $J:=\begin{pmatrix} 0 & E⃗_n \\ -E⃗_n & 0 \end{pmatrix}$ ).

(with being the unit vector).

The set of all symplectic matrices is a group, that is, has addition and multiplication and inversion with the usual properties.

Note that:

$\det T=1$

$J^{-1}=-J$

Author: Danny (remove the ".nospam" to send)

Last modification on: Sat, 04 May 2024 .