Abstract
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.
Partially supported by an NSF grant.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
H. Bart, I. Gohberg and M.A. Kaashoek: Minimal factorization of matrix and operator functions, Birkhäuser Verlag, Basel, 1979.
D.Z. Djokovic, J. Potera, P. Winteraitz and H. Zassenhaus: Normal forms of elements of classical real and complex Lie and Jordan algebras, Journal of Math. Physics 24 (1983), 1363–1374.
I. Gohberg, P. Lancaster and L. Rodman: Matrices and indefinite scalar products, Birkhäuser Verlag, Basel, 1983.
I. Gohberg, P. Lancaster and L. Rodman: Invariant subspaces of matrices with applications, J.Wiley, New York, 1986.
I. Gohberg and L. Rodman: On the distance between lattices of invariant subspaces, Linear Algebra Appl. 76 (1986), 85–120.
A.C.M. Ran and L. Rodman: Stable real invariant semidefinite subspaces and stable factorizations of symmetric rational matrix functions, Linear and
Multilinear Algebra 22 (1987), 25–55.
A.C.M. Ran and L. Rodman: Stability of invariant lagrangian subspaces I. Integral Equations and Operator Theory, to appear.
A.C.M. Ran and L. Rodman: Stability of invariant maximal semidefïnite subspaces I, Linear Algebra Appl. 62 (1984), 51–86.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Additional information
Dedicated to Professor Israel Gohberg on the occasion of his sixtieth birthday.
Rights and permissions
Copyright information
© 1989 Birkhäuser Verlag Basel
About this chapter
Cite this chapter
Ran, A.C.M., Rodman, L. (1989). Stability of Invariant Lagrangian Subspaces II. In: Dym, H., Goldberg, S., Kaashoek, M.A., Lancaster, P. (eds) The Gohberg Anniversary Collection. Operator Theory: Advances and Applications, vol 40/41. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-9144-8_13
Download citation
DOI: https://doi.org/10.1007/978-3-0348-9144-8_13
Publisher Name: Birkhäuser, Basel
Print ISBN: 978-3-0348-9924-6
Online ISBN: 978-3-0348-9144-8
eBook Packages: Springer Book Archive