Linear preservers of row-dense matrices

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

Czechoslovak Mathematical Journal, Tome 66 (2016) no. 3, pp. 847-858.

Résumé

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 $T:{\mathbf{M}}_{m,n}\to {\mathbf{M}}_{m,n}$ 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.

Détail

DOI : 10.1007/s10587-016-0296-4

Classification : 15A04, 15A21
Mots-clés : row-dense matrix; linear preserver; strong linear preserver