Terminology of "linear", "quadratic", etc. for multi-input functions

Question

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?

Answer 1

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.