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An Elementary Proof of the Frobenius Factorization Theorem for Differential Equations
Published online by Cambridge University Press: 20 November 2018
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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].
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- Copyright © Canadian Mathematical Society 1974