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Invariant subspaces of linear operators over R

Katarina Polc (2017) Invariant subspaces of linear operators over R. Diploma thesis.

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    Abstract

    In the thesis, we separate operators which have an effect on a vector space in such a way that they cause a decomposition of that space into a direct sum of minimal invariant subspaces. These kinds of operators are completely reducible. Invariant subspaces are then defined. We define induced operators that affect them to such extent that we can introduce their eigenspaces and root subspaces (generalized eigenspaces) and judge in which cases these are the same and what the consequences of that fact are. By using this procedure, we can separate the operators on those which cause a decomposition of space on only one-dimensional invariant subspaces and on those of which the decomposition of the space they affect on is different. The end result of this thesis is a treatment of the tool used to describe that kind of decomposition.

    Item Type: Thesis (Diploma thesis)
    Keywords: linear operator, invariant subspace, induced operator, eigenvalue, eigenspace, root subspace (generalized eigenspace)
    Number of Pages: 26
    Language of Content: Slovenian
    Mentor / Comentors:
    Mentor / ComentorsIDFunction
    prof. dr. Aleksander MalničMentor
    Link to COBISS: http://www.cobiss.si/scripts/cobiss?command=search&base=50126&select=(ID=11718473)
    Institution: University of Ljubljana
    Department: Faculty of Education
    Item ID: 4701
    Date Deposited: 20 Sep 2017 14:19
    Last Modified: 20 Sep 2017 14:19
    URI: http://pefprints.pef.uni-lj.si/id/eprint/4701

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