| Title:
|
Linear maps that strongly preserve regular matrices over the Boolean algebra (English) |
| Author:
|
Kang, Kyung-Tae |
| Author:
|
Song, Seok-Zun |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
61 |
| Issue:
|
1 |
| Year:
|
2011 |
| Pages:
|
113-125 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
The set of all $m\times n$ Boolean matrices is denoted by ${\mathbb M}_{m,n}$. We call a matrix $A\in {\mathbb M}_{m,n}$ regular if there is a matrix $G\in {\mathbb M}_{n,m}$ such that $AGA=A$. In this paper, we study the problem of characterizing linear operators on ${\mathbb M}_{m,n}$ that strongly preserve regular matrices. Consequently, we obtain that if $\min \{m,n\}\le 2$, then all operators on ${\mathbb M}_{m,n}$ strongly preserve regular matrices, and if $\min \{m,n\}\ge 3$, then an operator $T$ on ${\mathbb M}_{m,n}$ strongly preserves regular matrices if and only if there are invertible matrices $U$ and $V$ such that $T(X)=UXV$ for all $X\in {\mathbb M}_{m,n}$, or $m=n$ and $T(X)=UX^TV$ for all $X\in {\mathbb M}_{n}$. (English) |
| Keyword:
|
Boolean algebra |
| Keyword:
|
regular matrix |
| Keyword:
|
$(U,V)$-operator |
| MSC:
|
15A09 |
| MSC:
|
15A86 |
| MSC:
|
15B34 |
| idZBL:
|
Zbl 1224.15054 |
| idMR:
|
MR2782763 |
| DOI:
|
10.1007/s10587-011-0001-6 |
| . |
| Date available:
|
2011-05-23T12:35:09Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/141522 |
| . |
| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
|
[5] Moore, E. H.: General Analysis, Part I.Mem. of Amer. Phil. Soc. 1 (1935). |
| Reference:
|
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| Reference:
|
[7] Rao, P. S. S. N. V. P., Rao, K. P. S. B.: On generalized inverses of Boolean matrices.Linear Algebra Appl. 11 (1975), 135-153. Zbl 0322.15011, MR 0376706, 10.1016/0024-3795(75)90054-3 |
| Reference:
|
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| . |
