On the rational symplectic group

TL;DR

This paper provides a concise proof that any rational symplectic matrix can be diagonalized using integral symplectic matrices, simplifying the understanding of their structure.

Contribution

It offers a short, elegant proof of a classical result regarding the diagonalization of rational symplectic matrices using integral symplectic transformations.

Findings

Any rational symplectic matrix can be diagonalized with integral symplectic matrices.

The proof simplifies the classical understanding of the structure of rational symplectic matrices.

The result facilitates further analysis of symplectic groups over rational numbers.

Abstract

This note contains a short proof of a classical result: any rational symplectic matrix can be put in diagonal form after right and left multiplication by integral symplectic matrices.