Journal article
Rank Reducing Matrix Norms
Linear & multilinear algebra, v 50(2)
01 Jan 2002
Abstract
We consider approximation numbers for some norms on matrices, and look at the question when a closest rank h p approximant can be chosen to reduce the rank of a matrix by p . If the latter is always possible, we call the norm rank p reducing. It is easily seen that any unitarily invariant norm is rank p reducing. We show that any absolute norm on $\shadC^{n \times m}$ is rank n m 1 reducing and that the numerical radius norm on $ \shadC^{n\times n}$ is rank n m 1 reducing as well. Non-examples and computations of approximation numbers are also presented.
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Details
- Title
- Rank Reducing Matrix Norms
- Creators
- K. Okubo - Sapporo UniversityH.J. Woerdeman - William & Mary
- Publication Details
- Linear & multilinear algebra, v 50(2)
- Publisher
- Taylor & Francis Group
- Resource Type
- Journal article
- Language
- English
- Academic Unit
- Mathematics
- Web of Science ID
- WOS:000174911500011
- Scopus ID
- 2-s2.0-0036005509
- Other Identifier
- 991021866371404721
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- Collaboration types
- Domestic collaboration
- International collaboration
- Web of Science research areas
- Mathematics