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Nov 25, 2016 at 7:02 comment added user94803 Yes, your reduction shows that I was asking whether the entries of the matrix $A - \kappa diag(b_1,...,b_n)$. Actually the original intention was for the rank 1 matrices to have no zero rows.
Nov 25, 2016 at 5:14 comment added Pace Nielsen If Ilya interpreted your question correctly, the answer appears to be no. Try {{1/16, 1, 1}, {1, 1/2, 1}, {3/2, 1, 1}}.
Nov 24, 2016 at 16:17 comment added Ilya Bogdanov Each matrix with nonnegative entries is obviously a sum of rank 1 matrices with nonnegative entries (put each tow into a separate matrix). So you are asking just whether the entries of your matrix are nonnegative?
Nov 24, 2016 at 15:41 history asked user94803 CC BY-SA 3.0