MURAL - Maynooth University Research Archive Library



    On the Calculation of the l2→l1 Induced Matrix Norm


    Drakakis, Konstantinos and Pearlmutter, Barak A. (2009) On the Calculation of the l2→l1 Induced Matrix Norm. International Journal of Algebra, 3 (5). pp. 231-240. ISSN 1312-8868

    [img]
    Preview
    Download (124kB) | Preview


    Share your research

    Twitter Facebook LinkedIn GooglePlus Email more...



    Add this article to your Mendeley library


    Abstract

    We show that the l2 → l1 induced matrix norm, namely the norm induced by the l2 and l1 vector norms in the domain and range space, respectively, can be calculated as the maximal element of a finite set involving discrete additive combinations of the rows of the involved matrix with weights of ±1; the number of elements this set contains is exponential in the number of rows involved. A geometric interpretation of the result allows us to extend the result to some other induced norms. Finally, we generalize the findings to bounded linear operators on separable Banach spaces that can be obtained as strong limits of sequences of finite-dimensional linear operators.

    Item Type: Article
    Keywords: l2→l1 induced matrix norm, induced norms on Banach spaces
    Academic Unit: Faculty of Science and Engineering > Research Institutes > Hamilton Institute
    Item ID: 8176
    Depositing User: Barak Pearlmutter
    Date Deposited: 19 Nov 2018 17:54
    Journal or Publication Title: International Journal of Algebra
    Publisher: Hikari
    Refereed: Yes
    Funders: Science Foundation Ireland (SFI)
    URI:

    Repository Staff Only(login required)

    View Item Item control page

    Downloads

    Downloads per month over past year