TY - JOUR T1 - Scaling symmetric positive definite matrices to prescribed row sums JF - Linear Algebra and its Applications Y1 - 2003 A1 - O’Leary,Dianne P. KW - Diagonal preconditioning KW - Homotopy KW - Matrix scaling KW - Positive definite matrices AB - 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. VL - 370 SN - 0024-3795 UR - http://www.sciencedirect.com/science/article/pii/S0024379503003872 M3 - 10.1016/S0024-3795(03)00387-2 ER -