Advanced Search

Let ${𝐌}_{m,n}$ be the set of all $m\times n$ 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...