## We prove the spectral radius inequality ฯ(A for nonnegative matrices using the ideas of Horn and Zhang. We obtain the inequality A โข B ฯ(A T B) for nonnegative matrices, which improves Schur's classical inequality , where โข denotes the spectral norm. We also give counterexamples to two conject
Spectral variations and Hadamard products: Some problems
โ Scribed by Ren-Cang Li
- Publisher
- Elsevier Science
- Year
- 1998
- Tongue
- English
- Weight
- 558 KB
- Volume
- 278
- Category
- Article
- ISSN
- 0024-3795
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โฆ Synopsis
Many perturbation problems in matrix theory are related to three matrix minimization problems involving Hadamard products. Possible solutions to the problems are conjectured. The problems, if solved, may imply significant advances in eigenvalue, generalized eigenvalue variations, and perhaps in other aspects in matrix theory, too.
๐ SIMILAR VOLUMES
## Communicated by C. Bardos Abstract--ln this paper we give a simple representation of the solution of the Cauchy problem when the operator admits a spectral distribution. First we apply this to the Schr5dinger operator on R/v with and without potential, and then on a bounded domain. In this case