The reduction to normal form of a non-normal system of differential equations. De aequationum differentialium systemate non normali ad formam normalem revocando
Résumé
This paper was edited by Sigismund Cohn, C.W. Borchardt and A. Clebsch from posthumous manuscripts of C.G.J. Jacobi. The solution of the following problem: "to transform a square table of m^2 numbers by adding minimal numbers l_i to each horizontal row, in such a way that it possess m transversal maxima", determines the order and the shortest normal form reduction of he system: the equations u_i = 0 must be respectively diff erentiated l_i times. One also determines the number of di fferentiations of each equation of the given system needed to produce the differential equations necessary to reduce the proposed system to a single equation.
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