Take the 2-minute tour ×
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.

If $f(ta,tb) = f(a,b)$ $\forall t \neq 0$, then can we conclude that $f$ is a homogeneous polynomial of degree 1?

share|improve this question
    
All constant functions satisfy this. –  user1337 Nov 16 '13 at 20:12
    
Except constants, yes! –  Ehsan M. Kermani Nov 16 '13 at 20:13
    
A homogeneous degree $1$ polynomial would satisfy $f(ta, tb)=t^1 f(a, b)$. –  Macavity Nov 16 '13 at 20:18

1 Answer 1

Homogeneous of degree $1$ would be $f(ta,tb) = t^1f(a,b)$. In your case you have that $f(ta,tb) = f(a,b)=t^0f(a,b)$. This would mean homogeneous of degree $0$.

Here are some nice lecture notes and finer details on "functions homogeneous of degree $0$".

share|improve this answer

Your Answer

 
discard

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

Not the answer you're looking for? Browse other questions tagged or ask your own question.