On operator norms of submatrices |
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Authors: | Jorma Kaarlo Merikoski |
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Institution: | Department of Mathematical Sciences University of Tampere P.O. Box 607 SF-33101 Tampere 10, Finland |
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Abstract: | Both of the following conditions are equivalent to the absoluteness of a norm ν in n: (1) for all n×n diagonal matrices D=(dk), the subordinate operator norm Nν(D)=maxk|dk|; (2) for all n×n matrices A, Nν(A) ?Nν(|A|). These conditions are modified for partitioned matrices by replacing absolute values with norms of blocks. A generalization of absoluteness is thus obtained. |
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