publication . Article . 1992

Scalings of matrices satisfying line-product constraints and generalizations

Rothblum, U. G.; Zenios, Stavros A.; Rothblum, U. G.; Zenios, Stavros A.;
Open Access English
  • Published: 01 Oct 1992 Journal: Linear Algebra and its Applications (issn: 00243795, Copyright policy)
  • Publisher: Published by Elsevier Inc.
  • Country: Cyprus
Abstract A scaling of a nonnegative matrix A is a matrix having the form A ′ = UAV where U and V are square diagonal matrices which have positive diagonal elements. If the matrix A is square and V = U −1 , we call A ' a symmetric scaling of A . We consider two problems: the first concerns the identification of a scaling of a given nonnegative matrix with prescribed row and column products; the second concerns the problem of finding a symmetric scaling of a given nonnegative square matrix whose row products equal the corresponding column products. For each of these two scaling problems we characterize the solutions in terms of a nonlinear convex optimization prob...
free text keywords: Geometry and Topology, Algebra and Number Theory, Numerical Analysis, Discrete Mathematics and Combinatorics, Band matrix, Square matrix, Augmented matrix, Matrix (mathematics), Symmetric matrix, Skew-symmetric matrix, Block matrix, Mathematical analysis, Combinatorics, Mathematics, Nonnegative matrix
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