# Condition number of DA and D'A: row equilibrated matrix

I am with an exercise that first asks me to show that for any regular matrix $A$, there exists a diagonal matrix $D$ such that $A$ is transformed into a row equilibrated matrix by a left multiplication by $D$.

Next, I shall show that $K_\infty(DA)\leq K_\infty(CA)$ for any other diagonal matrix $C$, but I do not see how I can get there.

Can someone give a hint?

-best regards.

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Are the terms "regular matrix" and "row equilibrated matrix" standard? Wikiing for regular matrix gives me a disambiguation page: en.wikipedia.org/wiki/Regular_matrix. – Srivatsan Nov 13 '11 at 20:30
regular means invertible, $|A|$ nonzero. row equilibrated matrix means that the sum of the absolute values of the entries is the same in each row. – Marie. P. Nov 13 '11 at 21:18
Seen this? – J. M. Nov 13 '11 at 21:50