%0 Journal Article
%J Linear Algebra and its Applications
%D 2003
%T Scaling symmetric positive definite matrices to prescribed row sums
%A O’Leary,Dianne P.
%K Diagonal preconditioning
%K Homotopy
%K Matrix scaling
%K Positive definite matrices
%X We give a constructive proof of a theorem of Marshall and Olkin that any real symmetric positive definite matrix can be symmetrically scaled by a positive diagonal matrix to have arbitrary positive row sums. We give a slight extension of the result, showing that given a sign pattern, there is a unique diagonal scaling with that sign pattern, and we give upper and lower bounds on the entries of the scaling matrix.
%B Linear Algebra and its Applications
%V 370
%P 185 - 191
%8 2003/09/01/
%@ 0024-3795
%G eng
%U http://www.sciencedirect.com/science/article/pii/S0024379503003872
%R 10.1016/S0024-3795(03)00387-2