Scaling symmetric positive definite matrices to prescribed row sums
| Autor: | Dianne P. O'Leary |
|---|---|
| Rok vydání: | 2003 |
| Předmět: |
Numerical Analysis
Algebra and Number Theory Band matrix Diagonal preconditioning Symmetric rank-one Positive-definite matrix Combinatorics Definite quadratic form Sylvester's law of inertia Matrix scaling Diagonal matrix Discrete Mathematics and Combinatorics Symmetric matrix Homotopy Geometry and Topology Positive definite matrices Sign (mathematics) Mathematics |
| Zdroj: | Linear Algebra and its Applications. 370:185-191 |
| ISSN: | 0024-3795 |
| DOI: | 10.1016/s0024-3795(03)00387-2 |
| Popis: | 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. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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