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Assume $A$ is a positive definite matrix, and $B$ is a matrix with zero row sum.

Does matrix $A$ exist such that $AB$ is strictly diagonally dominant?

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How can a matrix with row sums $0$ be strictly diagonally dominant?

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  • $\begingroup$ B is zero row sum, but I am wondering, can we easily find a positive definite matrix that makes C=AB a strictly diagonally dominant? $\endgroup$ – Reza H. Khayyami Jun 5 '15 at 1:46
  • $\begingroup$ You don't understand. If $B$ has all row sums $0$, then so does $AB$. $\endgroup$ – Robert Israel Jun 5 '15 at 4:37
  • $\begingroup$ Thank you, you are right. A computational error had caused I keep getting a non-zero row sums. $\endgroup$ – Reza H. Khayyami Jun 5 '15 at 6:14

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