# Linear preservers of row-dense matrices

Sara M. Motlaghian; Ali Armandnejad; Frank J. Hall

Czechoslovak Mathematical Journal (2016)

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

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topMotlaghian, 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 - Armandnejad, Ali

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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