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Results tagged with eigenvalues
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user 21907
eigenvalues of matrices or operators
5
votes
Accepted
when is an eigenvalue differentiable with respect to a parameter?
When the roots are simple, they can be chosen as smooth functions of $\omega$ if the matrix $A$ is smooth of $\omega$ ; both "smooth" above can be replaced by "analytic". This is a consequence of the …
- 16.2k
0
votes
Relationship of eigenvalue/eigenvector of hermitian matrix R and QRQ (Q is diagonal)
I agree with the comments. However, there is a special case of interest, more general than commutation. Assume $R$ is a positive definite Hermitian matrix: this means that we can find a matrix $V$ suc …
- 16.2k
0
votes
0
answers
103
views
Numerical error on the spectrum of a matrix
I would like to find an upper bound for the absolute error on the eigenvalues of $Q$: we find numerically $\tilde\lambda_1,\dots, \tilde\lambda_N$ and if
$\lambda_1,\dots, \lambda_N$ are the eigenvalues …
- 16.2k
3
votes
Differentiability of eigenvalue and eigenvector on the non-simple case
Let me point out a more specific result for hyperbolic polynomials, known as Bronshtein's theorem (see e.g. the preprint https://arxiv.org/abs/1309.2150 by A. Parusinski & A. Rainer). Let $p(X,y)$ be …
- 16.2k
2
votes
Lower bound of the spectrum of a Schrodinger operator on a bounded domain
Bounds on the eigenvalues of the Laplace and Schrödinger operators.
Bull. Amer. Math. Soc., 82(5):751–753, 1976.
G. V. Rozenbljum. …
- 16.2k