| mots-clés : Histoire des mathématiques – philosophie des mathématiques – histoire des pratiques algébriques – didactique des mathéatiques – algèbre – arithmétique – mécanique – théorie spectrale – perspective historique dans l'enseignement des mathématiques – Jordan – Kronecker – Weierstrass – Frobenius – Autonne – Weyr – Cayley – Sylvester – Molien : Poincare – de Séguier – Lattès – formes bilinéaires – matrices – opérateurs – formes canoniques – invariants – décomposition – représentation. |
| autres localisations : http://fredericbrechenmacher.noosblog.fr |
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A history of the Jordan decomposition theorem (1870-1930)
Forms of representations and methods of decompositions. |
| The thesis takes as its point of departure the Jordan decomposition theorem and traces its evolution over the sixty-year period from its statement by Camille Jordan in 1870 to 1930 and the emergence of the theory of canonical matrices. A historical analysis of this particular theorem serves as a lens not only on internal developments of the evolving mathematics discipline of algebra but also on the external developments of mathematics as an internationalizing discipline in the decades around the turn of the twentieth century. The thesis draws from the study of networks of sources in order to analyze the theorem's transformation from a result in nineteenth-century group theory to one in the new twentieth century area of linear algebra, while, at the same time, the thesis explores issues of community formation and the role of tacit knowledge in the evolution of mathematical methods. The thesis will focus on a history the decomposition of matrices as a method of decomposition of a particular form of representation. |
| mots-clés en anglais : History of mathematics – philosophy of mathematics – algebra – arithmetics – spectral theory – didactic of mathematics – Jordan – Kronecker – Weierstrass – Frobenius – Autonne – Weyr – Cayley – Sylvester – Molien – Poincaré – de Séguier – Lattes – formes bilinéaires – matrices – opérateurs – formes canoniques – invariants – décomposition – représentation. |
