dimension

• December 6th 2009, 06:32 PM
Sampras
dimension
Call a polynomial balanced if its average value over every circle centered at zero is zero. The of all polynomials of degree $\leq 2009$ forms a vector space $V$. Find $\text{dim} \ V$.

So what basis this you use?
• December 6th 2009, 06:43 PM
Sampras
Quote:

Originally Posted by Sampras
Call a polynomial balanced if its average value over every circle centered at zero is zero. The of all polynomials of degree $\leq 2009$ forms a vector space $V$. Find $\text{dim} \ V$.

So what basis this you use?

I used rank nullity.
• December 7th 2009, 03:53 AM
Raoh
the set of polynomials with degree less or equal a certain natural $n$,is a subspace with dimension equal to $n+1$.