Google/ read upon this concept if not familiar. JL Lemma: Given a set S ofn vectors in d-dimensional space, there exists a random k X d matrix H where k = 0(log n/ez) , such that for any x E S (1 )|le|: 3 \"Fix\": 3 (1+ )||x||: with probability at least 1 i. Each entry of the matrix H is an independent Gaussian. n3 In this problem, a different random matrix is considered as follows. For each i E {1, ...,n} we pick a uniformly random number hi E {1, ..., k}. We then set \"hij = i1 for each i E {1, ...,n} (the sign is chosen uniformly at random from {1, 1}), and 2 all other entries of H are set to 0. Show that for this H, ||Hx| |2 is an unbiased estimator of IIxIIj