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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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    Are the terms "regular matrix" and "row equilibrated matrix" standard? Wikiing for regular matrix gives me a disambiguation page: http://en.wikipedia.org/wiki/Regular_matrix.2011-11-13
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    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.2011-11-13
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    Seen [this](http://books.google.com/books?id=mlOa7wPX6OYC&pg=PA125)?2011-11-13

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