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Lemma: Uniqueness Lemma of a Finite Basis
If \(B\) is a finite basis of a vector space \(V\) then each vector \(v\in V\) can be uniquely represented as a linear combination of finitely many elements of \(B\) (i.e. the basis vectors).
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References
Bibliography
 Koecher Max: "Lineare Algebra und analytische Geometrie", SpringerVerlag Berlin Heidelberg New York, 1992, 3rd Volume