| 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:
|
http://hdl.handle.net/10338.dmlcz/119467 |
| . |
| 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 |
| . |
