Thursday, 27 October 2011

random matrices - Probability on the distance

Let A be an ntimesn gaussian matrix whose entries are i.i.d.
copies of a gaussian variable, and leftajrightnj=1
be the column vectors of A. How to show that the probability
mathbbPleft(dgeqtright)leqCect
for some c,C>0 and every t>0, where d is the distance between
a1 and the n1-dimensional subspace spanned by a2,cdots,an.



Thanks a lot!

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