- #1

tunafish

- 11

- 0

Let's take a function [itex]f:\mathbb{R}^n\rightarrow \mathbb{R}[/itex].

And so [itex]f(x_1,x_2,...,x_n)=y; \;\;y\in \mathbb{R}[/itex]

It's of course a function of many variables, but can this be considered a function of a vector whose components are the [itex]x_n[/itex]'s?

And if it actually is a function of a vector, in which way are the basis involved?

For example if we take function [itex]f(x,y)=x+y[/itex] is it intended that we are working with

[itex]f(x,y)=x\vec{e}_x+y\vec{e}_y[/itex] ?

If so why then the result [itex]f(x,y)[/itex] is a scalar? And how could i put togheter the coefficient of different vectors??

But most of all..where are the basis vectors gone? Thanks for your help!

(ps: if this is NOT a function of vectors could you make me an example of one which is??)