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In this expository note, we give a modern proof of Hanson-Wright inequality for quadratic forms in sub-gaussian random variables.We deduce a useful concentration inequality for sub-gaussian random vectors.Two examples are given to illustrate these results: a concentration of distances between random vectors and subspaces, and a bound on the norms of products of random and deterministic matrices.
Rudelson et al. (Tue,) studied this question.