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The Convergence of a Subspace Trajectory for an Arbitrary Operator

In: Dynamical Systems Generated by Linear Maps

Author

Listed:
  • Ćemal B. Dolićanin

    (State University of Novi Pazar)

  • Anatolij B. Antonevich

    (Belarusian State University)

Abstract

If the operator $$A$$ A has only one eigenvalue, then the limit of the trajectory $$A^n(V)$$ A n ( V ) exists for any subspace $$V$$ V . BUt, iIn the general case, the limit of trajectory can does not exist, and the question is: what is the conditions on the subspaces $$V$$ V , whose validity implies the existence of the limit of the trajectory. In this chapter, we discuss this problem for an arbitrary linear invertible operator $$A$$ A in a $$m$$ m -dimensional complex space $$X$$ X .

Suggested Citation

  • Ćemal B. Dolićanin & Anatolij B. Antonevich, 2014. "The Convergence of a Subspace Trajectory for an Arbitrary Operator," Springer Books, in: Dynamical Systems Generated by Linear Maps, edition 2, chapter 0, pages 141-155, Springer.
    • Handle: RePEc:spr:sprchp:978-3-319-08228-8_12
    DOI: 10.1007/978-3-319-08228-8_12
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