Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

Suppose the map $u:(\mathbb{R}^{|A|})^{n} \rightarrow \mathbb{R}^{|A|}$ can be written in an additive form, i.e. there exist real-valued functions $g_{i}$ s.t.

$u(x_{1},\dots,x_{n})=\sum g_{i}(x_{1},\dots,x_{n})x_{i}$

where each $x_{i}\in \mathbb{R}^{|A|}$. We can think of each $g_{i}(x_{1},\dots,x_{n})$ as being the "weight" corresponding to $x_{i}$.

When is it the case that each weight depends only on the vector to which the weight corresponds? That is, when is it the case that we can also write, for some real-valued $f_{i}$ (for $i=1,\dots ,n$)

$u(x_{1},\dots,x_{n})=\sum f_{i}(x_{i})x_{i}$ ?

Thanks in advance

share|cite|improve this question
Is $|A|$ finite? And is it $>n$? – ronno Oct 27 '12 at 19:04
(Thanks for the clarifying question.) $|A|$ is finite and yes if you'd like, take $|A|>n$. – Kenny LJ Oct 31 '12 at 16:48

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Browse other questions tagged or ask your own question.