Geodesic
An Elementary Proof of the Jordan--Kronecker Theorem
Matematičeskie zametki, Tome 94 (2013) no. 6, pp. 857-870.

Voir la notice de l'article provenant de la source Math-Net.Ru

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. 
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I. K. Kozlov. An Elementary Proof of the Jordan--Kronecker Theorem. Matematičeskie zametki, Tome 94 (2013) no. 6, pp. 857-870. http://geodesic.mathdoc.fr/item/MZM_2013_94_6_a5/

[1] A. V. Bolsinov, A. A. Oshemkov, “Bi-Hamiltonian structures and singularities of integrable systems”, Regul. Chaotic Dyn., 14:4-5 (2009), 431–454 | DOI | MR

[2] I. M. Gelfand, I. S. Zakharevich, “Spektralnaya teoriya puchka kososimmetricheskikh differentsialnykh operatorov 3-go poryadka na $S^1$”, Funkts. analiz i ego pril., 23:2 (1989), 1–11 | MR | Zbl

[3] F. J. Turiel, “Classification locale simultanée de deux formes symplectiques compatibles”, Manuscripta Math., 82:3-4 (1994), 349–362 | DOI | MR

[4] F. J. Turiel, On the Local Theory of Veronese Webs, arXiv: math.DG/1001.3098v1

[5] F. J. Turiel, The Local Product Theorem for Bihamiltonian Structures, arXiv: math.SG/1107.2243v1

[6] I. S. Zakharevich, Kronecker Webs, Bihamiltonian Structures, and the Method of Argument Translation, arXiv: math.SG/9908034v3

[7] A. S. Mischenko, A. T. Fomenko, “Uravneniya Eilera na konechnomernykh gruppakh Li”, Izv. AN SSSR. Ser. matem., 42:2 (1978), 396–415 | MR | Zbl

[8] A. S. Mischenko, A. T. Fomenko, “Obobschennyi metod Liuvillya integrirovaniya gamiltonovykh sistem”, Funkts. analiz i ego pril., 12:2 (1978), 46–56 | MR | Zbl

[9] A. T. Fomenko, “O simplekticheskikh strukturakh i integriruemykh sistemakh na simmetricheskikh prostranstvakh”, Matem. sb., 115:2 (1981), 263–280 | MR | Zbl

[10] F. R. Gantmakher, Teoriya matrits, Nauka, M., 1988 | MR | Zbl

[11] R. C. Thompson, “Pencils of complex and real symmetric and skew matrices”, Linear Algebra Appl., 147 (1991), 323–371 | DOI | MR