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Results tagged with positivity
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user 102946
7
votes
Accepted
Strong positivity of Neumann Laplacian
As other users have indicated in the comments, for sufficiently smooth domains one can get it by combining, for instance, elliptic regularity with Hopf's boundary point lemma (and then go from the ell …
- 12.5k
58
votes
Accepted
Is this proof of Perron's theorem correct, and if so is it original?
The OP's subsequent argument (which proves algebraic simplicity) actually shows the following general spectral theoretic observation (which is independent of any positivity assumptions): If $\lambda$ is … a geometrically simple eigenvalue of a matrix $A$ and if there exists an eigenvector $\Psi$ and a dual eigenvector $\Pi$ such that $\Pi\Psi \not= 0$, then $\lambda$ is also algebraically simple (positivity …
- 12.5k