Abstract
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×n nonnegative matrix and let X and Y be n×n diagonal matrices having positive diagonal elements. Then the matrices XA, XAX−1 and XAY are 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.Key wordsMatrix Scalings
Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
