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Definition: Affine Basis, Affine Coordinate System

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 \(V_A\).

Table of Contents

Corollaries: 1

1. Definition: Bounded Affine Set

Mentioned in:

Corollaries: 1
Definitions: 2
Proofs: 3

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References

Bibliography

1. Wille, D; Holz, M: "Repetitorium der Linearen Algebra", Binomi Verlag, 1994