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 -