Line-sum-symmetric Scalings of Square Nonnegative Matrices
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چکیده
A square matrix is called line-sum-symmetric if the sum of elements in each of its rows equals the sum of elements in the corresponding column. Let A be an n x n nonnegative matrix and let X and Y be n x n diagonal matrices having positive diagonal elements. Then the matrices XA, XAXand XA Yare called a row-scaling, a similarity-scaling and an equivalence-scaling of A. The purpose of this paper is to study the different forms of line-sum-symmetric scalings of square nonnegative matrices. In particular, we characterize matrices for which such scalings exist and show uniqueness of similarity-scalings and uniqueness of row-scalings, up to a scalar mUltiple of the blocks corresponding to the classes of the given matrix.
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تاریخ انتشار 1985