Terminology of "linear", "quadratic", etc. for multi-input functions It is my understanding that, according to typical math terminology:


*

*The function $f(x, y) = x + y$ is "linear".
Specifically, it's linear in both $x$ and $y$, but this is understood implicitly.  

*The function $g(x, y) = x^2 + y^2$ is "quadratic".
Specifically, it's quadratic in both $x$ and $y$, but this is understood implicitly.


But what's $h(x, y) = x \times y$?
Is it correct to call it "linear"? Is it correct to call it "quadratic"?
It seems to me that $h$ is "linear" if $x$ and $y$ are independent, or "quadratic" if $x = y$.
So I'm not sure what I'm supposed to call it. Is there a standard terminology for it?

The function $h(x, y) = xy$ is called "bilinear". It is a special case of a quadratic function which, when considered as a function of one variable at a time, is linear.
