# Thread:

1. ## 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?

2. 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.

3. the set of polynomials with degree less or equal a certain natural $n$,is a subspace with dimension equal to $n+1$.
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