As we all know, correlation is a statistical relationship between two random variables. However, if there are two non-random variables, is there correlation between them, if it has, how to describe it mathematically.
More specially, in random sense, we have $cov\{x,y\}$ to describe the correlation between two random variables, when it comes to two non-random variables, let's denote them as $x$ and $y$, all of them are bounded by a certain region, for example $x^T P_x x\leq 1$, $y^T P_y y\leq 1$, ($P_x, P_y$ are available), then, what's the correlation between them? how to describe it mathematically?