## Abstract We consider Hamiltonian matrices obtained by means of symmetric and positive definite matrices and analyse some perturbations that maintain the eigenvalues on the imaginary axis of the complex plane. To obtain this result we prove for such matrices the existence of a diagonal form or, a
A relative perturbation bound for positive definite matrices
✍ Scribed by Roy Mathias; Krešimir Veselić
- Publisher
- Elsevier Science
- Year
- 1998
- Tongue
- English
- Weight
- 202 KB
- Volume
- 270
- Category
- Article
- ISSN
- 0024-3795
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✦ Synopsis
We give a sharp estimate for the eigenvectors of a positive definite Hermitian matrix under a floating-point perturbation. The proof is elementary.
📜 SIMILAR VOLUMES
We consider the problem of identifying all determinantal inequalities valid on all positive definite matrices. This is fundamentally a combinatorial problem about relations between collections of index sets. We describe some general structure of this problem and give sufficient and necessary conditi
We give a bound for the perturbations of invariant subspaces of graded indefinite Hermitian matrix H = D \* AD which is perturbed into H + δH = D \* (A + δA)D. Such relative perturbations include an important case where H is given with an element-wise relative error. Application of our bounds requir