Annali di Matematica Pura ed Applicata

, Volume 51, Issue 1, pp 147–160 | Cite as

Reduction of systems of linear differential equations to jordan normal form

  • Mary L. Cartwright


Various methods are discussed of finding a non-singular matrix P such that PAP−1=J, where J is theJordan normal form of A, with special reference to the problem of reducing the system of equations x=Ax to the form y=Jy, where y=Px.


Differential Equation Normal Form Special Reference Linear Differential Equation 
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  1. (1).
    SeeCoddington andLevinson,Theory of Ordinary Differential Equations (1955), Chapter 3,G. Sansone andR. Conti,Equazioni Differenziali Non Lineari (Rome 1956), Chapter VIII,V. V. Nemitsky andV. V. Stepanof,Qualitative theory of differential equations, 2nd ed. Moscow 1949.Google Scholar
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    The two following sections are based onO. Schreier andE. Sperner,Introduction to Modern Algebra and Matrix Theory, translated byM Davis andM. Hausner, (New York 1951) 344–371 where further details of the algebraic processes will be found.Google Scholar
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    SeeJ. A. Todd, loc. cit. 152–4.Google Scholar

Copyright information

© Swets & Zeitlinger B. V. 1960

Authors and Affiliations

  • Mary L. Cartwright
    • 1
  1. 1.Cambridge

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