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Apr 7, 2011 at 9:06 comment added Benoît Kloeckner I think the question has potential, but the discussion below Aaron Meyerowitz' answer makes a point: the question is not precise enough as it is.
Apr 5, 2011 at 22:28 comment added Aaron Meyerowitz I like the question. I never voted to close it but I did vote to reopen it as soon as it closed. I haven't seen more reopen votes since then.
Apr 5, 2011 at 17:06 history edited Seva CC BY-SA 2.5
Formatting
Apr 5, 2011 at 16:04 history edited Seva CC BY-SA 2.5
deleted 39 characters in body; edited tags
Apr 5, 2011 at 13:41 comment added Seva @Aaron: I intentionally do not want to ask the question about a specific subspace. What if tomorrow I need another subspace? This is a general, and perfectly legitimate, question about the tools and results that can be useful to attack a special kind of problem. I made it very clear now that I am looking at the ratio, and I am not going to post essentially the same question a second time. Instead, I would expect those who voted for closing to vote for re-opening now. I think it is absolutrely clear to everybody that my question is not "less real" than other MO questions.
Apr 5, 2011 at 13:12 comment added Aaron Meyerowitz I suggest re-editing or posting a new question with a description of the invariant subspace L and the clarification that you want the ratio.
Apr 5, 2011 at 6:53 comment added Seva @fedja: I explained above what I mean by "relatively small". As to you last remark: if the subspace is aligned with some coordinate plane, then it most certainly does not have the property in question. Loosely speaking, what I need is a criterion to show that a subspace is not aligned with the coordinate planes!
Apr 5, 2011 at 6:50 comment added Seva @Bill: I believe, it is reasonable to request background for extremely specialized and artificially looking questions. This is certainly not the case with a general question like this. The question is motivated by my attempt to construct a graph with some particular property, but I am certainly not in a position to describe here all the work which led me to this question.
Apr 5, 2011 at 6:47 history edited Seva CC BY-SA 2.5
Explanations inserted
Apr 5, 2011 at 4:49 history closed Bill Johnson
Igor Rivin
fedja
Andreas Thom
Daniel Litt
not a real question
Apr 5, 2011 at 4:47 answer added Aaron Meyerowitz timeline score: 1
Apr 5, 2011 at 3:14 comment added fedja I second Bill's vote. I don't care much about the background but a legitimate question should be far more precise than this. As of now, I do not even understand what "relatively small" might mean here. Indeed, no vector is longer than $\sqrt n$ and, unless your subspace is more or less aligned with some coordinate plane of small dimension, there is little chance to get much less for the maximal projection.
Apr 4, 2011 at 21:47 answer added Igor Rivin timeline score: 0
Apr 4, 2011 at 20:39 comment added Bill Johnson Please state a reasonable question and give background. As is, I vote to close.
Apr 4, 2011 at 20:17 history asked Seva CC BY-SA 2.5