Let \(\mathcal A=(A,V_A,v)\) be an affine space. Any \(n+1\) affinely independent points. \[P_0,P_1,P_2\ldots,P_n\quad\quad ( * )\]
are called an affine basis (or an affine coordinate system) of \(\mathcal A\).
Equivalently, \( ( * ) \) is an affine basis, if the \(n\) vectors
\[x_1=\overrightarrow{P_0P_1},\,x_2=\overrightarrow{P_0P_2},\,\ldots,\,x_n=\overrightarrow{P_0P_n}\]
form a basis of the corresponding vector space \(V_A\).
Corollaries: 1
Corollaries: 1
Definitions: 2
Proofs: 3