# relationship between number of polynomials and dimension of the space.

If $$p_1,p_2,...,p_k$$ are linearly independent polynomials in $$P_n$$, a mathematical relationship between $$k$$ and $$n$$ is:

$$k\le n.$$

If the k will be more than n, the set of polynomials cannot be linearly independent, is it correct?

## 1 Answer

If by $P_n$ you mean the polynomials of degree $\le n$, then your relation should be $k \le n+1$: for example, $1 (= x^0), x^1, \ldots, x^n$ is a basis. It follows that a set of more than $n+1$ members of $P_n$ cannot be linearly independent.