Date: 31 Mar 2009

The reduction to normal form of a non-normal system of differential equations

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Abstract

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 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 the system: the equations u i = 0 must be respectively differentiated i times. One also determines the number of differentiations of each equation of the given system needed to produce the differential equations necessary to reduce the proposed system to a single equation.

C. G. J. Jacobi deceased on 1851.