Article
Bounds on the spectral radius of a Hadamard product of nonnegative or positive semidefininte matrices
Electronic Journal of Linear Algebra
Document Type
Article
Publication Date
2-1-2010
Keywords
- Hadamard product,
- Nonnegative matrix,
- Positive semidefinite matrix,
- Positive definite matrix,
- Spectral radius,
- Kronecker product,
- Matrix inequality
Disciplines
Abstract
X. Zhan has conjectured that the spectral radius of the Hadamard product of two square nonnegative matrices is not greater than the spectral radius of their ordinary product. We prove Zhan’s conjecture, and a related inequality for positive semidefinite matrices, using standard facts about principal submatrices, Kronecker products, and the spectral radius
DOI
10.13001/1081-3810.1359
Citation Information
Fuzhen Zhang and Roger A. Horn. "Bounds on the spectral radius of a Hadamard product of nonnegative or positive semidefininte matrices" Electronic Journal of Linear Algebra Vol. 20 (2010) p. 90 - 94 ISSN: 1081-3810 Available at: http://works.bepress.com/fuzhen-zhang/26/
AMS subject classifications. 15A45, 15A48, 15A69