bio | website | tx.technion.ac.il/~felixg/… |
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location | ||
age | 31 | |
visits | member for | 3 years, 1 month |
seen | Apr 14 at 0:34 | |
stats | profile views | 3,258 |
Apr 5 |
comment |
Does this inequality always hold?
So, what is the motivation/context for this conjecture? |
Apr 1 |
comment |
How large can a set of nearly equidistant points be?
@BenoîtKloeckner I am more interested in $\epsilon>\frac{1}{n-1}$ and fixed. |
Apr 1 |
revised |
How large can a set of nearly equidistant points be?
edited title |
Apr 1 |
comment |
How large can a set of nearly equidistant points be?
@BillJohnson JL says that if I have such a set in a higher dimension $n \approx e^{k}$ , then I can embed it into $\mathbb{R}^{k}$ while (almost) preserving the distance property. But I don't see how it guarantees the existence of such a set to begin with. Am I missing something here? P.S. JL does not assume anything on the relation of the pairwise distances to each other, while in this case I need to. P.P.S. The question actually originates in an attempt to understand a result related to JL. :) |
Apr 1 |
asked | How large can a set of nearly equidistant points be? |
Mar 28 |
comment |
What are the external triumphs of matroid theory?
Can you share it now...? |
Mar 16 |
asked | power laws emerging from the sandpile model |
Mar 10 |
awarded | Yearling |
Feb 25 |
comment |
When does a d.r.v. take a value very close to the mean?
@Suvrit Yes, sort of. These are the volumes of all $n \times k$ submatrices of a fixed $n \times m$ matrix. |
Feb 25 |
asked | When does a d.r.v. take a value very close to the mean? |
Feb 4 |
awarded | Notable Question |
Feb 3 |
comment |
Rank changes with matrix edits
@Turbo Yes, I think it does. |
Feb 3 |
comment |
Rank changes with matrix edits
@Turbo In that case, things are open again.... :( If you want to discuss the specific case, feel free to email me. |
Feb 3 |
comment |
Rank changes with matrix edits
@Turbo Yes, all you need is Hermitianness of $M$ and $W$. But as I said, having $\{0,1\}$ helps to perhaps pinpoint precisely which of the three cases occurs. |
Feb 3 |
comment |
Rank changes with matrix edits
@Turbo The magic works because it's a rank 1 update. It's possible to use interlacing for rank $k$ updates, but the bounds get progressively weaker, of course. The proof for rank $k$ is just an inductive application of Corollary 4.3.9 $k$ times (decompose $W$ as the sum of $k$ matrices of rank $1$). |
Feb 3 |
comment |
Rank changes with matrix edits
@Turbo It's proved in the reference I gave (the standard one on the subject). |
Feb 3 |
comment |
Rank changes with matrix edits
Btw, why the extremal-combinatorics tag? Is there an interesting application you have in mind? |
Feb 3 |
answered | Rank changes with matrix edits |
Feb 2 |
revised |
An exact fraction of a matrix
edited body |
Feb 2 |
comment |
An exact fraction of a matrix
@AllenKnutson $M$ is $A$. Fixing now, Thanks. |