Elementary proof of Jordan-Kronecker theorem

TL;DR

This paper provides a straightforward proof of the Jordan-Kronecker theorem, establishing a canonical form for pairs of skew-symmetric bilinear forms over algebraically closed fields.

Contribution

It offers an elementary proof of the Jordan-Kronecker theorem, simplifying understanding of canonical forms for skew-symmetric form pairs.

Findings

Proves the Jordan-Kronecker theorem with an elementary approach.

Establishes a canonical form for pairs of skew-symmetric bilinear forms.

Applicable over algebraically closed fields.

Abstract

In this paper we prove the Jordan-Kronecker theorem which gives a canonical form for a pair of skew-symmetric bilinear forms on a finite-dimensional vector space over an algebraically closed field.