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Definition: Dimension of an Affine Space

The dimension \(\operatorname {dim}(\mathcal A)\) of an affine space \(\mathcal A=(A,V_A,v)\) is the dimension of the corresponding vector space \(V_A\):

\[\operatorname {dim}(\mathcal A):=\operatorname {dim}(V_A)\]

Note: If \(\operatorname {dim}(V_A)\) is finite, say \(n\), then this means that we need \(n+1\) affinely independent points. \[P_0,P_1,P_2\ldots,P_n\] to form an affine basis of \(\mathcal A\).

Table of Contents

1. Definition: Points, Lines, Planes, Hyperplanes

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Corollaries: 1
Definitions: 2 3 4 5 6 7 8
Proofs: 9

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References

Bibliography

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