How to say ${f : V \times V \to \mathbb{R}}$

Question

I've googled like a nut trying to get an explanation for the following notation:

${f : V \times V \to \mathbb{R}}$

As I read it: "the function $f$ that maps from the Cartesian product of vector V and V to a real number", i.e. the inner product of a vector space or dot product.

I'd appreciate confirmation on my assumption on how to read the notation.

Thanks

Answer 1

In simply means that $f$ is a function from the Cartesian product of $V$ by itself into the set $\Bbb R$ of real numbers. It doesn't have to be an inner product. You could have, say, $V=\Bbb R$ and $f(x,y)=xe^{x+\cos(y)}-y$.