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An Elementary Proof of the Frobenius Factorization Theorem for Differential Equations

Published online by Cambridge University Press:  20 November 2018

E. W. Kennedy
E. W. Kennedy*
Affiliation:
Department of Mathematics, Calif. Polytechnic State University, San Luis Obispo, Ca 93401, USA
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Consider the 1st order linear system

1

when An(t) is real valued and continuous on I, ai, i+1(t) ≠ 0, aij(t) ≡ 0 for j ≥ i + 2, t ∊ I and i = 1, …, n — l. In what follows, components cj of a vector c will be identifiable by the superscript. The purpose of this note is to give a simple induction proof of the following theorem of Frobenius [1].

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 17 , Issue 3 , 01 September 1974 , pp. 379 - 380
Copyright
Copyright © Canadian Mathematical Society 1974

References

1. Frobenius, G., Ueber die Déterminante mehrerer Funktionen einer Variablen, J. Reine Angew. Math. 77 (1874), 245-257.Google Scholar
2. Hartman, P., Ordinary differential equations, Wiley, New York, 1964.Google Scholar