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Mar 26, 2015 at 2:36 answer added RoyS timeline score: 1
Mar 14, 2015 at 7:45 comment added ttb Thanks for this example. It seems that you can use the same argument for the identity matrix, and then you can conclude that $P(\|A\| = \|B\|)$ is going to be high for other matrix norms which specialize to the the largest absolute element on diagonal matrices.
Mar 12, 2015 at 4:50 comment added Christian Remling I don't think you can say a whole lot for general $A$. For example, if there's a single column with $1$'s only and all other entries are zero, then $\|B\|=\|A\|$ with prob $1-(1-\rho)^n$, so the expectation doesn't go down by much.
Mar 12, 2015 at 4:28 history asked ttb CC BY-SA 3.0