Bounds on the spectral radius of a Hadamard product of nonnegative or positive semidefinite matrices
ELA. The Electronic Journal of Linear Algebra, Tome 20 (2010), pp. 90-94.

Voir la notice de l'article dans Electronic Library of Mathematics

Summary: 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.
Classification : 15A45, 15A48, 15A69
Mots-clés : Hadamard product, nonnegative matrix, positive semidefinite matrix, positive definite matrix, spectral radius, Kronecker product, matrix inequality 
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     author = {Horn, Roger A. and Zhang, Fuzhen},
     title = {Bounds on the spectral radius of a {Hadamard} product of nonnegative or positive semidefinite matrices},
     journal = {ELA. The Electronic Journal of Linear Algebra},
     pages = {90--94},
     publisher = {mathdoc},
     volume = {20},
     year = {2010},
     language = {en},
     url = {https://geodesic-test.mathdoc.fr/item/EEJLA_2010__20__a48/}
}
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Horn, Roger A.; Zhang, Fuzhen. Bounds on the spectral radius of a Hadamard product of nonnegative or positive semidefinite matrices. ELA. The Electronic Journal of Linear Algebra, Tome 20 (2010), pp. 90-94. https://geodesic-test.mathdoc.fr/item/EEJLA_2010__20__a48/