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An matrix with nonnegative entries is called row stochastic if the sum of entries on every row of is 1. Let be the set of all real matrices. For , we say that is row Hadamard majorized by (denoted by if there exists an row stochastic matrix such that , where is the Hadamard product (entrywise product) of matrices . In this paper, we consider the concept of row Hadamard majorization as a relation on and characterize the structure of all linear operators preserving (or...
Let be the set of all real or complex matrices. For , we say that is row-sum majorized by (written as ) if , where is the row sum vector of and is the classical majorization on . In the present paper, the structure of all linear operators preserving or strongly preserving row-sum majorization is characterized. Also we consider the concepts of even and circulant majorization on and then find the linear preservers of row-sum majorization of these relations on .
Let be the set of all real matrices. A matrix 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 that preserve or strongly preserve row-dense matrices, i.e., is row-dense whenever is row-dense or is row-dense if and only if is row-dense, respectively. Similarly, a matrix is called a column-dense matrix if every column of is a column-dense vector. At the end, the structure of linear...
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