Affine space/Barycentric coordinates/Definition

Barycentric coordinates

Let ${}P_{i}$, ${}i\in I$, denote an affine basis in an affine space ${}E$ over the ${}K$-vector space ${}V$. For a point ${}P\in E$, the uniquely determined numbers

$(a_{i},i\in I){\text{ with }}\sum _{i\in I}a_{i}=1$

such that

${}P=\sum _{i\in I}a_{i}P_{i}\,$

holds, are called the barycentric coordinates of ${}P$.