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
| Original language | American English |
|---|---|
| Pages (from-to) | 90-94 |
| Number of pages | 5 |
| Journal | Electronic Journal of Linear Algebra |
| Volume | 20 |
| DOIs | |
| State | Published - Jan 1 2010 |
ASJC Scopus Subject Areas
- Algebra and Number Theory
Keywords
- Hadamard product
- Kronecker product
- Matrix inequality
- Nonnegative matrix
- Positive definite matrix
- Positive semidefinite matrix
- Spectral radius
Disciplines
- Mathematics
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