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Some inequalities for generalized eigenvalues of perturbation problems on Hermitian matrices
Yan Hong1, Dongkyu Lim2, Feng Qi3,4,5
11College of Mathematics, Inner Mongolia University for Nationalities, Tongliao, China.
Journal of Inequalities and Applications
|August 24, 2018
Summary
Researchers established new inequalities for generalized eigenvalues in Hermitian matrix perturbation problems. These findings improve upon existing inequalities for generalized eigenvalues in the literature.
Area of Science:
- Linear Algebra
- Matrix Theory
- Numerical Analysis
Background:
- Generalized eigenvalues are crucial in analyzing matrix perturbations.
- Existing inequalities for generalized eigenvalues have limitations.
Purpose of the Study:
- To establish novel inequalities for generalized eigenvalues of perturbed Hermitian matrices.
- To address and rectify shortcomings in current generalized eigenvalue inequalities.
Main Methods:
- Analysis of perturbation problems involving Hermitian matrices.
- Development of new mathematical inequalities.
Main Results:
- New inequalities for generalized eigenvalues were successfully established.
- The proposed inequalities overcome limitations of prior results.
Conclusions:
- The paper provides significant advancements in the theory of generalized eigenvalues for perturbed Hermitian matrices.
- These new inequalities offer improved analytical tools for researchers in the field.
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