Question about notation in Matrix problem

[mcah5]

Hello,

I'm somewhat confused about the notation in problem 4c of http://www.its.caltech.edu/~hmabuchi/Ph125a/HW1.pdf

In part a, I found the matrix R. I was wondering what was meant by a,b exist in R. My guess is that R in the latter case refers to the set of all real numbers, and that the R in v = a*R + b*R^2 is the matrix R corresponding to the observable r.

Could somebody confirm, or am I totally off?

Also, I'm not sure how to intepret what v is.

 

[jonestr]

a and b are elements of the real numbers so I think your first statement was correct. If we say that R tells how the probabilities combine to get the expecation value then I think that R^2 will tell us about how the squares of the probabilites will add which tells us about the dispersion of the measure. I am not 100% sold on this since usually the disperson is given as <x>^2-<x^2> (maybe off by a sign here.) so the lack of a square post expectation value is discerning

Tom

 

[mcah5]

Ok, thanks!