Ok, so I've been trying to read up on how SVM's work and started with maximal margin classifiers. At page $132$ in ESL (Elements of Statistical Learning) the authors "reformulates" the optimization problem but I can't seem to understand what they are doing from $(4.47)$ to $(4.48)$. Does anyone know?
Here is an excerpt:
Edit: I guess, what I don't understand is why we can arbitrarly set the magnitude of beta to $\frac1M$. What does a positively scaled multiple mean in this case? Just a multiple larger than $0$?