0 : Guest Lecture by Venkat Guruswami : Euclidean Subspaces and Compressed Sensing
نویسندگان
چکیده
where the second inequality follows from Cauchy-Schwartz. Furthermore, the CauchySchwartz inequality holds with equality for all vectors x in the one-dimensional subspace spanned by the all-ones vector. Therefore, it is not difficult to achieve Property 1 when the subspace X has small dimension. But we want the dimension to be very large, let us say, dim(X) = Ω(N). As it turns out, even with this additional requirement, such subspaces exist. In fact, in a certain sense most subspaces of dimension, say, N/2 satisfy the desired property.
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