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broken link fixed, cf. https://meta.mathoverflow.net/q/5301/70594
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Glorfindel
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Take $n\ll N$. Let $P$ be an $n\times N$ matrix of iid $\mathcal{N}(0,1)$ random variables, and let $D$ be an $N\times N$ diagonal matrix.

What can be said about the distribution of the largest singular value of $PD$?

When $n=1$, I get concentration inequalities from Lemma 1 of this paperthis paper. I would like a probabilistic upper bound for the general case, and I wouldn't be surprised if this is already available in the literature.

Take $n\ll N$. Let $P$ be an $n\times N$ matrix of iid $\mathcal{N}(0,1)$ random variables, and let $D$ be an $N\times N$ diagonal matrix.

What can be said about the distribution of the largest singular value of $PD$?

When $n=1$, I get concentration inequalities from Lemma 1 of this paper. I would like a probabilistic upper bound for the general case, and I wouldn't be surprised if this is already available in the literature.

Take $n\ll N$. Let $P$ be an $n\times N$ matrix of iid $\mathcal{N}(0,1)$ random variables, and let $D$ be an $N\times N$ diagonal matrix.

What can be said about the distribution of the largest singular value of $PD$?

When $n=1$, I get concentration inequalities from Lemma 1 of this paper. I would like a probabilistic upper bound for the general case, and I wouldn't be surprised if this is already available in the literature.

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Dustin G. Mixon
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What is the spectral norm of a random projection times a diagonal?

Take $n\ll N$. Let $P$ be an $n\times N$ matrix of iid $\mathcal{N}(0,1)$ random variables, and let $D$ be an $N\times N$ diagonal matrix.

What can be said about the distribution of the largest singular value of $PD$?

When $n=1$, I get concentration inequalities from Lemma 1 of this paper. I would like a probabilistic upper bound for the general case, and I wouldn't be surprised if this is already available in the literature.