# Linear preservers of row-dense matrices

• Volume: 66, Issue: 3, page 847-858
• ISSN: 0011-4642

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## Abstract

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Let ${𝐌}_{m,n}$ be the set of all $m×n$ real matrices. A matrix $A\in {𝐌}_{m,n}$ 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 $T:{𝐌}_{m,n}\to {𝐌}_{m,n}$ that preserve or strongly preserve row-dense matrices, i.e., $T\left(A\right)$ is row-dense whenever $A$ is row-dense or $T\left(A\right)$ is row-dense if and only if $A$ is row-dense, respectively. Similarly, a matrix $A\in {𝐌}_{n,m}$ 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.

## How to cite

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Motlaghian, Sara M., Armandnejad, Ali, and Hall, Frank J.. "Linear preservers of row-dense matrices." Czechoslovak Mathematical Journal 66.3 (2016): 847-858. <http://eudml.org/doc/286793>.

@article{Motlaghian2016,
abstract = {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.},
author = {Motlaghian, Sara M., Armandnejad, Ali, Hall, Frank J.},
journal = {Czechoslovak Mathematical Journal},
keywords = {row-dense matrix; linear preserver; strong linear preserver},
language = {eng},
number = {3},
pages = {847-858},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Linear preservers of row-dense matrices},
url = {http://eudml.org/doc/286793},
volume = {66},
year = {2016},
}

TY - JOUR
AU - Motlaghian, Sara M.
AU - Hall, Frank J.
TI - Linear preservers of row-dense matrices
JO - Czechoslovak Mathematical Journal
PY - 2016
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 66
IS - 3
SP - 847
EP - 858
AB - 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.
LA - eng
KW - row-dense matrix; linear preserver; strong linear preserver
UR - http://eudml.org/doc/286793
ER -

## References

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