The Convergence of a Subspace Trajectory for an Arbitrary Operator

Ćemal B. Dolićanin () and Anatolij B. Antonevich ()
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Ćemal B. Dolićanin: State University of Novi Pazar
Anatolij B. Antonevich: Belarusian State University

Chapter Chapter 12 in Dynamical Systems Generated by Linear Maps, 2014, pp 141-155 from Springer

Abstract: 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 .

Keywords: Invariant Subspace; Algebraic Approach; Special Numeration; Grassmann Manifold; Jordan Form (search for similar items in EconPapers)
Date: 2014
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-319-08228-8_12

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DOI: 10.1007/978-3-319-08228-8_12

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