Can you suggest a reference where I can find some detail about Plucker relations ? It would help if you can suggest something which has a few examples.

@Sheikraisinrollbank Thank you this is very useful for my purpose, as you have guessed correctly I am not looking for an algorithm to computationally check it.

I know that's kind of a worst case scenario. I am hoping when $m$ and $n$ are comparable, for example when $n=m+1$ or $m+2$ one can do much better. I feel there is a lot of redundancy in these cases.

Thanks @Yemon it was my inability to nail down the exact source of the screeching sound :-) and I ended up adding more noise am afraid, but then that's the way I learn I suppose, and for me that's the point

@Yemon Choi Did you notice the title now is in fact a answer to the question itself :)

point taken, I made that statement to emphasize that it matters a lot what notion of distance (if you like topolgy) we are considering when we are talking about convergence... so just saying two sequence converges without clarifying what the notion of convergence is inadequate. The title now edited by Yemon Choi is in fact the perfect answer to the original question which incidentally was "two sequences converge to each other"

how can we talk about convergence without a notion of distance ?

@sandeepj it really looks interesting! thank you.

@Qiaochu Yuan Thanks for the reference. I am interested in understanding the results related to zero multiplicity.