A controversy and the writing of a history: the discussion of "small oscillations" (1760-1860) from the standpoint of the controversy between Jordan and Kronecker (1874)
Résumé
In 1874, a strong controversy on the theory of bilinear and quadratic forms opposed Camille Jordan and Leopold Kronecker. The arithmetical ideal of Kronecker faced Jordan's claim for the simplicity of his algebraic canonical form. As the controversy combined mathematical and historical arguments, it gave rise to the writing of a history of the methods used by Lagrange, Laplace and Weierstrass in a century long mathematical discussion (1760-1860) around the "equation of secular inequalities".
Mots clés
invariant factors
History of mathematics
philosophy ofmathematics
history of algebra
generality
Jordan
Kronecker
Lagrange
Laplace
Cauchy
Frobenius
Weierstrass
linear algebra
spectral theory
mechanics
arithmetic
bilinear forms
group theory
differential equations
matrices
canonical form
elementary divisors
invariant factors.
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