论文信息 - Scaling symmetric positive definite matrices to prescribed row sums

Scaling symmetric positive definite matrices to prescribed row sums

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.

Dianne P. O'Leary | D. O’Leary

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