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Title: Monotonicity of the maximum of inner product norms (English)
Author: Lavrič, Boris
Language: English
Journal: Commentationes Mathematicae Universitatis Carolinae
ISSN: 0010-2628 (print)
ISSN: 1213-7243 (online)
Volume: 45
Issue: 3
Year: 2004
Pages: 383-388
Category: math
Summary: Let $\Bbb K$ be the field of real or complex numbers. In this note we characterize all inner product norms $p_1,\ldots ,p_m$ on $\Bbb K^n$ for which the norm $x\longmapsto \max \{p_1(x),\ldots ,p_m(x)\}$ on $\Bbb K^n$ is monotonic. (English)
Keyword: finite dimensional vector space
Keyword: monotonic norm
Keyword: absolute norm
Keyword: inner pro\-duct norm
MSC: 15A60
MSC: 15A63
MSC: 52A21
idZBL: Zbl 1100.15013
idMR: MR2103134
Date available: 2009-05-05T16:45:58Z
Last updated: 2012-04-30
Stable URL:
Reference: [1] Bauer F.L., Stoer J., Witzgall C.: Absolute and monotonic norms.Numer. Math. 3 (1961), 257-264. Zbl 0111.01602, MR 0130104
Reference: [2] Horn R.A., Johnson C.R.: Matrix Analysis.Cambridge University Press, New York, 1985. Zbl 0801.15001, MR 0832183
Reference: [3] Johnson C.R., Nylen P.: Monotonicity properties of norms.Linear Algebra Appl. 148 (1991), 43-58. Zbl 0717.15015, MR 1090752
Reference: [4] Lavrič B.: Monotonicity and $ ^*$orthant-monotonicity of certain maximum norms.Linear Algebra Appl. 367 (2003), 29-36. Zbl 1038.15017, MR 1976908


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