◀ ▲ ▶Branches / Algebra / Definition: Basis, Coordinate System
Definition: Basis, Coordinate System
A subset \(B\) of a vector space \(V\neq \{0\}\) is called a basis (or a coordinate system) if
 \(B\) is a generating system of \(V\),
 Any finitely many vectors of \(B\) are linearly independent.
In other words, \(B\) is a set of linearly independent vectors that, in a linear combination, can represent every vector in \(V\). The elements of the \(B\) are called basis vectors.
Table of Contents
 Lemma: Uniqueness Lemma of a Finite Basis
 Theorem: Finite Basis Theorem
Mentioned in:
Definitions: 1 2 3 4 5
Explanations: 6
Lemmas: 7 8
Parts: 9 10
Proofs: 11 12 13 14
Theorems: 15
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References
Bibliography
 Koecher Max: "Lineare Algebra und analytische Geometrie", SpringerVerlag Berlin Heidelberg New York, 1992, 3rd Volume
 Wille, D; Holz, M: "Repetitorium der Linearen Algebra", Binomi Verlag, 1994