In some situations we have access to a representation like this:


$ f(x,y) = \sum\_i u\_i(x) v\_i(y) $


What is this called? (I know when you jam this into PDE get to call it 'separation of variables' but I'm sure it's got a different name in pure math).



Multivariate expansion in terms of single variate products: what is the name for this?
[This paper](http://www.jstor.org/discover/10.2307/2688535?uid=3737536&uid=2129&uid=2&uid=70&uid=4&sid=21101713553267) calls it "separable of rank $n$" if $n$ is the number of terms in the sum. If the sum is an infinite one, the condition is very weak (for example it includes all functions with a convergent Taylor expansion).


