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Results tagged with perturbation-theory
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user 8799
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Eigenvalue-related statements
This is rather classical. The set of such $\lambda$'s is called the $\epsilon$-pseudo-spectrum. It is presented in many books on numerical linear algebra. I suggest S.K. Godunov Modern aspects of line …
- 52.3k
2
votes
Bounding eigenvalue/eigenspace perturbations for hermitian matrices
The eigenvalues are $1$-Lipschitz over the set of Hermitian matrices:
$$|\lambda_k(B)-\lambda_k(A)\|\le\|B-A\|.$$
This Lipschitz property is a very different phenomenon than the analyticity of $t\maps …
- 52.3k
20
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Differentiability of Eigenvalues - Perturbation Theory
The complete reference is Kato's book Perturbation theory .... But perhaps you need only the most basic results. Then see my book Matrices (Springer GTM #216), 2nd edition. This is Section 5.2.
Mind …
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