| Title:
|
Row Hadamard majorization on ${\bf M}_{m,n}$ (English) |
| Author:
|
Askarizadeh, Abbas |
| Author:
|
Armandnejad, Ali |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
71 |
| Issue:
|
3 |
| Year:
|
2021 |
| Pages:
|
743-754 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
An $m \times n$ matrix $R$ with nonnegative entries is called row stochastic if the sum of entries on every row of $R$ is 1. Let ${\bf M}_{m,n}$ be the set of all $m \times n$ real matrices. For $A,B\in \nobreak {\bf M}_{m,n}$, we say that $A$ is row Hadamard majorized by $B$ (denoted by $A\prec _{RH}B)$ if there exists an $m \times n$ row stochastic matrix $R$ such that $A=R\circ B$, where $X \circ Y$ is the Hadamard product (entrywise product) of matrices $X,Y\in {\bf M}_{m,n}$. In this paper, we consider the concept of row Hadamard majorization as a relation on ${\bf M}_{m,n}$ and characterize the structure of all linear operators $T\colon {\bf M}_{m,n} \rightarrow {\bf M}_{m,n}$ preserving (or strongly preserving) row Hadamard majorization. Also, we find a theoretic graph connection with linear preservers (or strong linear preservers) of row Hadamard majorization, and we give some equivalent conditions for these linear operators on ${\bf M}_{n}$. (English) |
| Keyword:
|
linear preserver |
| Keyword:
|
row Hadamard majorization |
| Keyword:
|
row stochastic matrix |
| MSC:
|
15A04 |
| MSC:
|
15A21 |
| idZBL:
|
07396194 |
| idMR:
|
MR4295242 |
| DOI:
|
10.21136/CMJ.2020.0081-20 |
| . |
| Date available:
|
2021-08-02T08:05:05Z |
| Last updated:
|
2023-10-02 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/149053 |
| . |
| Reference:
|
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| Reference:
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| Reference:
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| Reference:
|
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| Reference:
|
[5] Hasani, A. M., Radjabalipour, M.: The structure of linear operators strongly preserving majorization of matrices.Electron. J. Linear Algebra 15 (2006), 260-268. Zbl 1145.15003, MR 2255479, 10.13001/1081-3810.1236 |
| Reference:
|
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| . |
