Scaling symmetric positive definite matrices to prescribed row sums

✍ Scribed by Dianne P. O’Leary

• Publisher: Elsevier Science
• Year: 2003
• Tongue: English
• Weight: 85 KB
• Volume: 370
• Category: Article
• ISSN: 0024-3795
• DOI: 10.1016/s0024-3795(03)00387-2

✦ Synopsis

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.