| Title:
|
Linear preservers of row-dense matrices (English) |
| Author:
|
Motlaghian, Sara M. |
| Author:
|
Armandnejad, Ali |
| Author:
|
Hall, Frank J. |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
66 |
| Issue:
|
3 |
| Year:
|
2016 |
| Pages:
|
847-858 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
Let $\mathbf {M}_{m,n}$ be the set of all $m\times n$ real matrices. A matrix $A\in \mathbf {M}_{m,n}$ is said to be row-dense if there are no zeros between two nonzero entries for every row of this matrix. We find the structure of linear functions $T\colon \mathbf {M}_{m,n} \rightarrow \mathbf {M}_{m,n}$ that preserve or strongly preserve row-dense matrices, i.e., $T(A)$ is row-dense whenever $A$ is row-dense or $T(A)$ is row-dense if and only if $A$ is row-dense, respectively. Similarly, a matrix $A\in \mathbf {M}_{n,m}$ is called a column-dense matrix if every column of $A$ is a column-dense vector. At the end, the structure of linear preservers (strong linear preservers) of column-dense matrices is found. (English) |
| Keyword:
|
row-dense matrix |
| Keyword:
|
linear preserver |
| Keyword:
|
strong linear preserver |
| MSC:
|
15A04 |
| MSC:
|
15A21 |
| idZBL:
|
Zbl 06644037 |
| idMR:
|
MR3556871 |
| DOI:
|
10.1007/s10587-016-0296-4 |
| . |
| Date available:
|
2016-10-01T15:27:46Z |
| Last updated:
|
2023-10-28 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/145875 |
| . |
| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
|
[6] Pierce, S., Lim, M. H., Lowey, R., Li, Ch.-K., Tsing, N.-K., McDonald, B. R., Basley, L.: A survey of linear preserver problems.Linear Multilinear Algebra 33 (1992), 1-129. 10.1080/03081089208818176 |
| Reference:
|
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| . |
