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Results tagged with eigenvalues
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user 398
eigenvalues of matrices or operators
3
votes
Eigenvalue of a convolution and a restriction?
Let me simultaneously (a) show why it is clear to me that user548030 is an AI, (b) work through some issues raised in its answer.
The first paragraph of user548030's answer restates (correctly) one o …
- 20.2k
1
vote
From one eigenvector to many, in a very local graph?
Here is my self-answer to (c), based on my self-answer to (b).
For any $f:V\to \mathbb{C}$ with $|f|_2^2=1$ and $|\langle f,\Delta f\rangle|\geq \alpha>0$, we obtain, proceeding as in my self-answer t …
- 20.2k
1
vote
From one eigenvector to many, in a very local graph?
Let me show how to do (b), in a more general context than I set out in (b).
Let $f:V\to \mathbb{C}$ with $|f|_2=1$ and $|\langle f, \Delta f\rangle|\geq \alpha>0$.
Consider a partition of $V$ inducing …
- 20.2k
3
votes
If many orthogonal vectors are respected (somewhat), are there many eigenvectors with large ...
Actually, isn't question 2 brutally trivial? The following argument seems to show that the space $W$ spanned by the eigenspaces with eigenvalue $\geq \delta$ has dimension $\geq k$.
Suppose this were …
- 20.2k