This article is cited in 4 papers

An Elementary Proof of the Jordan–Kronecker Theorem

I. K. Kozlov

M. V. Lomonosov Moscow State University

Abstract: This paper presents a proof of the Jordan–Kronecker theorem on the reduction to canonical form of a pair of skew-symmetric bilinear forms on a finite-dimensional linear space over an algebraically closed field.

Keywords: Jordan–Kronecker theorem, skew-symmetric bilinear form, Jordan block, Kronecker block, algebraically closed field, finite-dimensional linear space, self-adjoint operator, symplectic space, Lagrange subspace.

UDC: 512.647.2

Received: 16.12.2011
Revised: 26.12.2012

DOI: 10.4213/mzm9303

 English version: Mathematical Notes, 2013, 94:6, 885–896

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