I have the following problem. A is a sum of independent random matrices and B is some fixed positive (semi-)definite matrix. I'm interested in a bound on the expectation of the operator norm $\lVert BA(I+BA)^{-1}\rVert$. Is there anything easy to say about this ? Alternatively $\lVert (I+BA)^{-1}\rVert$ should do it as well.
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2Is there a particular distribution you are choosing the random matrices from? – muaddib Jun 04 '15 at 16:20
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well i wouldn't want to use that type of information if possible but gaussian with some non-linearities on top. – Cdi Jun 04 '15 at 16:26