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.