Question

What does the notation
\[ V(v_1, v_2)= f(v_1,v_2) (v_1+v_2) \]
mean? What does the notation
\[ V(v_1, v_2)= f(v_1,v_2) (v_1+v_2) \]
mean? @Mathematics

Answer 1

Context is important here but it looks like V is a function
V : W x W --> W
where W is a vector space

and f is function

f : W x W --> Reals (or whatever the scalars are here.)

Answer 2

So what does it mean? Could you give an example?

Answer 3

I can, but again, the context in which you find all of this is important as my hypothesis may not be right.

Here's an example given my hypothesis. Let
\[ f : \mathbb{R}^3 \times \mathbb{R}^3 \to \mathbb{R} \]
be defined by
\[ (v_1,v_2) \mapsto v_1 . v_2 \ \hbox{, the inner product/dot product} \]

Then we could define a function
\[ V : \mathbb{R}^3 \times \mathbb{R}^3 \to \mathbb{R}^3 \]
by
\[ V(v_1,v_2) = f(v_1,v_2) (v_1 + v_2) \]

Answer 4

Hmm I think I misunderstood the actual text:) thanks for your help though :) I figured out what I did wrong as well:)