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Definition: Euclidean Affine Space
An affine space \((A,V_A,v)\) is called an Euclidean affine space, if \(V_A\) is a vector space over the field of real numbers \(\mathbb R\) and a real scalar product \(\langle\cdot,\cdot\rangle\) is defined on \(V_A\).
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References
Bibliography
 Wille, D; Holz, M: "Repetitorium der Linearen Algebra", Binomi Verlag, 1994