Stability of Invariant Lagrangian Subspaces II

  • André C. M. Ran
  • Leiba Rodman
Part of the Operator Theory: Advances and Applications book series (OT, volume 40)


In this paper we consider various stability properties of real invariant lagrangian subspaces for real matrices which are either symmetric or skew-symmetric in a real quadratic form which may be symmetric or skew-symmetric itself. In particular, apart from ordinary stability we shall consider strong stability, which seems to be more desirable from a numerical point of view. For the classes of matrices we consider here stable subspaces are not always strongly stable, in contrast with the previous work. We shall completely characterize strongly stable invariant lagrangian subspaces, and in many cases also the stable ones. Invariant lagrangian subspaces with other stability properties, such as Lipschitz stability, are characterized as well.


Invariant Subspace Real Eigenvalue Real Matrice Strong Stability Stable Element 
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Copyright information

© Birkhäuser Verlag Basel 1989

Authors and Affiliations

  • André C. M. Ran
    • 1
  • Leiba Rodman
    • 2
  1. 1.Faculteit Wiskunde en InformaticaVrije UniversiteitAmsterdamThe Netherlands
  2. 2.Department of MathematicsCollege of William and Mary in VirginiaWilliamsburgUSA

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