# Multivariate expansion in terms of single variate products: what is the name for this?

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).

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The function $f$ is called separable in some other circumstances too. Like my masters thesis and a number of game theory references therein (none of which have anything to do with PDE). –  Noah Stein Jan 25 '13 at 23:14

This paper 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).