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Mat. Zametki, 2013, Volume 94, Issue 6, Pages 857–870 (Mi mz9303)  

This article is cited in 3 scientific papers (total in 3 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.

DOI: https://doi.org/10.4213/mzm9303

Full text: PDF file (504 kB)
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English version:
Mathematical Notes, 2013, 94:6, 885–896

Bibliographic databases:

UDC: 512.647.2
Received: 16.12.2011
Revised: 26.12.2012

Citation: I. K. Kozlov, “An Elementary Proof of the Jordan–Kronecker Theorem”, Mat. Zametki, 94:6 (2013), 857–870; Math. Notes, 94:6 (2013), 885–896

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. A. Bolsinov, A. Izosimov, “Singularities of bi-Hamiltonian systems”, Comm. Math. Phys., 331:2 (2014), 507–543  crossref  mathscinet  zmath  adsnasa  isi
    2. I. K. Kozlov, “Invariant foliations of nondegenerate bi-Hamiltonian structures”, J. Math. Sci., 225:4 (2017), 596–610  mathnet  crossref  mathscinet  elib
    3. V. A. Bovdi, T. G. Gerasimova, M. A. Salim, V. V. Sergeichuk, “Reduction of a pair of skew-symmetric matrices to its canonical form under congruence”, Linear Alg. Appl., 543 (2018), 17–30  crossref  mathscinet  zmath  isi
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