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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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    Seen [this](http://books.google.com/books?id=mlOa7wPX6OYC&pg=PA125)?2011-11-13

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