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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
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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) |
| Related URLs: | |
| URI: | https://mural.maynoothuniversity.ie/id/eprint/8176 |
| Use Licence: | This item is available under a Creative Commons Attribution Non Commercial Share Alike Licence (CC BY-NC-SA). Details of this licence are available here |
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