# Discriminant analysis: When does correlation improve discrimination?

In Multivariate Analysis (Mardia et al, pg 324), the authors write

"it might be thought that a linear combination of two variables would provide a better discriminator if they were correlated than if they were uncorrelated".

Before studying the problem, why would one hypothesize this? My guess (which was incorrect) is that uncorrelated variables may discriminate better because they are not redundant.

My question is not about the proof against statement above. Rather: why does Mardia propose that the readers may have expected what is written above when I am guessing the opposite?

I don't have the book at hand at present, so I can't be sure what the authors meant and in what context. I will surmise that they are speaking of the most straightforward evidence. And the key is that they - I suppose - talk about some single linear combination, that is, single variable derived from two variables. "a linear combination of two variables would provide a better discriminator if they were correlated than if they were uncorrelated".