Affine space/Barycentric coordinates/Points/Example

Let ${}P_{i}$, ${}i\in I$, be an affine basis in an affine space ${}E$ over the ${}K$-vector space ${}V$. Then the point ${}P_{j}$ (${}j=I$) has the barycentric coordinates ${}(0,\ldots ,0,1,0,\ldots ,0)$, where the ${}1$ is at the ${}j$-th place (${}I$ being finite and ordered).