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Let A be $n\times m$ matrix with independent identical distributed rows $X_i$valued \in $R^m$. Let $Q \in R^m$ be orthogonal projection. Suppose, Euclidean norm $P(\lVert QX_i\rVert_2^2>t)<\frac{1}{t^a}$, for some $t>rank Q $.

Is it possible to find a bound $\lVert A\rVert_2$ in terms of norm $\lVert QX_i\rVert$?

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This doesn't make sense to me. Are $r^m$ and $R^m$ supposed to be ${\mathbb R}^m$? If $Q$ is a projection, it's not a member of ${\mathbb R}^m$. And why would you think $\|A\|_2$ would be determined by the norms of a projection of its rows? –  Robert Israel Feb 6 '12 at 23:08
Thank you . I corrected my question. –  Nick G.H. Feb 7 '12 at 4:02

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