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
Article
  • 129 Downloads

Summary

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.

Keywords

Differential Equation Normal Form Special Reference Linear Differential Equation 

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Bibliografia

  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
  2. (2).
    SeeSansone andConti, p. 543 footnote 11.Google Scholar
  3. (3).
    E. Coddington andLevinson, Perturbations of linear systems with constaut coefficients possessing periodic solutions,Contributions to the theory of non-linear oscillations, Vol 2, edS. Lefschetz, « Annals of Maths Studies », 29, 1952, 19–35,H. L. Turritin, Asymptotic expansions of solutions of systems of ordinary differential equations containing a parameter,loc. cit, 81–116,P. Mendelson, On phase portraits of critic 1 points in -space,Contributions to the theory of non-linear oscillations, Vol. 4, edS. Lefschetz, « Annals of Maths Studies », 41 (1958), 167–199,D. Bushaw,Differential equations with a discontinuous forcing term, Experimental Towing Tank, Stevens Institute of Technology No. 469 (1953),Z. Szmydt, On th degree of regularity of surfaces formed by the asymptotic integrals of differential equations, « Annales Polonici Mathematici », II 2 (1955), 294–313.Google Scholar
  4. (4).
    SeeJ. A. Todd,Projective and analytical geometry, (London 1947), 166.Google Scholar
  5. (5).
    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
  6. (7).
    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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