Affine space/Affine basis/Definition

Affine basis

A family of points ${}P_{i}\in E$, ${}i\in I$, in an affine space ${}E$ over a ${}K$-vector space ${}V$ is called an affine basis of ${}E$, if there exists an ${}i_{0}\in I$ such that the family of vectors

${\overrightarrow {P_{i_{0}}P_{i}}},i\in I\setminus \{i_{0}\},$

is a basis of ${}V$.