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Results tagged with perturbation-theory
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user 121665
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$C^1$ perturbation of diffeomorphism is diffeomorphism?
Assuming that $M$ is a compact manifold, the answer is yes. Indeed, $\det Df(x)\neq 0$ for $x\in M$ and if $|Df(x)-Df_\epsilon(x)|$ is small, then $\det Df_\epsilon(x)\neq 0$, because the set of inver …
- 28k
9
votes
Differentiability of Eigenvalues - Perturbation Theory
Eigenvalues are roots of the characteristic polynomial. In the case the polynomial has simple roots, they smoothly depend on the coefficients. Below is the proof in the real case. The argument below c …
- 28k