Linear preservers of row-dense matrices
Czechoslovak Mathematical Journal, Tome 66 (2016) no. 3, pp. 847-858.
Voir la notice de l'article dans Czech Digital Mathematics Library
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.
DOI :
10.1007/s10587-016-0296-4
Classification :
15A04, 15A21
Mots-clés : row-dense matrix; linear preserver; strong linear preserver
Mots-clés : row-dense matrix; linear preserver; strong linear preserver
@article{10_1007_s10587_016_0296_4, author = {Motlaghian, Sara M. and Armandnejad, Ali and Hall, Frank J.}, title = {Linear preservers of row-dense matrices}, journal = {Czechoslovak Mathematical Journal}, pages = {847--858}, publisher = {mathdoc}, volume = {66}, number = {3}, year = {2016}, doi = {10.1007/s10587-016-0296-4}, mrnumber = {3556871}, zbl = {06644037}, language = {en}, url = {https://geodesic-test.mathdoc.fr/articles/10.1007/s10587-016-0296-4/} }
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 SP - 847 EP - 858 VL - 66 IS - 3 PB - mathdoc UR - https://geodesic-test.mathdoc.fr/articles/10.1007/s10587-016-0296-4/ DO - 10.1007/s10587-016-0296-4 LA - en ID - 10_1007_s10587_016_0296_4 ER -
%0 Journal Article %A Motlaghian, Sara M. %A Armandnejad, Ali %A Hall, Frank J. %T Linear preservers of row-dense matrices %J Czechoslovak Mathematical Journal %D 2016 %P 847-858 %V 66 %N 3 %I mathdoc %U https://geodesic-test.mathdoc.fr/articles/10.1007/s10587-016-0296-4/ %R 10.1007/s10587-016-0296-4 %G en %F 10_1007_s10587_016_0296_4
Motlaghian, Sara M.; Armandnejad, Ali; Hall, Frank J. Linear preservers of row-dense matrices. Czechoslovak Mathematical Journal, Tome 66 (2016) no. 3, pp. 847-858. doi : 10.1007/s10587-016-0296-4. https://geodesic-test.mathdoc.fr/articles/10.1007/s10587-016-0296-4/
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