Weighted l∞ norms for matrices
| Autor: | Richard Arens, Moshe Goldberg |
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| Rok vydání: | 1994 |
| Předmět: | |
| Zdroj: | Linear Algebra and its Applications. 201:155-163 |
| ISSN: | 0024-3795 |
| DOI: | 10.1016/0024-3795(94)90112-0 |
| Popis: | Let W = ( w ij ) be a fixed n × n matrix of positive entries, and consider the W -weighted l ∞ norm defined on C n×n by ‖A‖w, ∞ = max| i, j | w ij α ij |, A =( α ij ).The main purpose of this note is to prove that for this norm, multiplicativity, strong stability, and quadrativity are each equivalent to the condition ( W -1 ) 2 ⩽ W -1 , where W -1 = ( ω -1 ij ) is the Hadamard inverse of W . Among other things we also show that if ‖ · ‖ ∞ is k -bounded for some k ⩾ 2, then it is stable. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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