| Title:
|
On row-sum majorization (English) |
| Author:
|
Akbarzadeh, Farzaneh |
| Author:
|
Armandnejad, Ali |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
69 |
| Issue:
|
4 |
| Year:
|
2019 |
| Pages:
|
1111-1121 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
Let $\mathbb {M}_{n,m}$ be the set of all $n\times m$ real or complex matrices. For $A,B\in \mathbb {M}_{n,m}$, we say that $A$ is row-sum majorized by $B$ (written as $A\prec ^{\rm rs} B$) if $R(A)\prec R(B)$, where $R(A)$ is the row sum vector of $A$ and $\prec $ is the classical majorization on $\mathbb {R}^n$. In the present paper, the structure of all linear operators $T\colon \mathbb {M}_{n,m}\rightarrow \mathbb {M}_{n,m}$ preserving or strongly preserving row-sum majorization is characterized. Also we consider the concepts of even and circulant majorization on $\mathbb {R}^n$ and then find the linear preservers of row-sum majorization of these relations on $\mathbb {M}_{n,m}$. (English) |
| Keyword:
|
majorization |
| Keyword:
|
linear preserver |
| Keyword:
|
doubly stochastic matrix |
| MSC:
|
15A04 |
| MSC:
|
15A21 |
| idZBL:
|
07144880 |
| idMR:
|
MR4039625 |
| DOI:
|
10.21136/CMJ.2019.0084-18 |
| . |
| Date available:
|
2019-11-28T08:53:07Z |
| Last updated:
|
2022-01-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/147919 |
| . |
| Reference:
|
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| Reference:
|
[2] Armandnejad, A., Heydari, H.: Linear preserving $gd$-majorization functions from $M_{n,m}$ to $M_{n,k}$.Bull. Iran. Math. Soc. 37 (2011), 215-224. Zbl 1237.15021, MR 2850115 |
| Reference:
|
[3] Bhatia, R.: Matrix Analysis.Graduate Texts in Mathematics 169, Springer, New York (1997). Zbl 0863.15001, MR 1477662, 10.1007/978-1-4612-0653-8 |
| Reference:
|
[4] Hasani, A. M., Radjabalipour, M.: The structure of linear operators strongly preserving majorizations of matrices.Electron. J. Linear Algebra 15 (2006), 260-268. Zbl 1145.15003, MR 2255479, 10.13001/1081-3810.1236 |
| Reference:
|
[5] Motlaghian, S. M., Armandnejad, A., Hall, F. J.: Linear preservers of Hadamard majorization.Electron. J. Linear Algebra 31 (2016), 593-609. Zbl 1347.15005, MR 3578394, 10.13001/1081-3810.3281 |
| Reference:
|
[6] Soleymani, M., Armandnejad, A.: Linear preservers of circulant majorization on $\mathbb{R}^n$.Linear Algebra Appl. 440 (2014), 286-292. Zbl 1286.15033, MR 3134271, 10.1016/j.laa.2013.10.040 |
| Reference:
|
[7] Soleymani, M., Armandnejad, A.: Linear preservers of even majorization on $M_{n,m}$.Linear Multilinear Algebra 62 (2014), 1437-1449. Zbl 1309.15045, MR 3261749, 10.1080/03081087.2013.832487 |
| . |
