Timeline for Comparison of the norm of a matrix and its entry-wise absolute value.
Current License: CC BY-SA 3.0
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| Oct 1, 2012 at 8:11 | comment | added | Mikael de la Salle | In fact I also found the counterexamples with the help of a computer: I first looked at matrices with entries in $\{{-1,0,1\}}$. I then realized that all the counterexamples produced this way had exactly 2 nonzero entries on each row and column. I therefore looked at matrices of the form $1_n+P$ for a permutation matrix $P$ with signs, and realized that these were counterexamples when $P'$ was of order $n$. The only thing that remained was to find a proof. | |
| Sep 30, 2012 at 15:02 | history | answered | Suvrit | CC BY-SA 3.0 |