Geodesic
Linear preservers of row-dense matrices
Czechoslovak Mathematical Journal, Tome 66 (2016) no. 3, pp. 847-858 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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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.
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
Keywords: row-dense matrix; linear preserver; strong linear preserver 
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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

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