I am sucked by a very simple question. I want to find an element which minimizes the$\|A\|$(in $L^2$-norm ),where A is a random variable. Then the textbook says the uniqueness will follow from strict convexity of the $L^2$ norm.
What does this mean? What should I do if I want to prove the uniqueness? I think it may be very easy but I just don't know how to start.
