◀ ▲ ▶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

1. Lemma: Uniqueness Lemma of a Finite Basis
2. 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

Thank you to the contributors under CC BY-SA 4.0!

Github:

References

Bibliography

1. Koecher Max: "Lineare Algebra und analytische Geometrie", Springer-Verlag Berlin Heidelberg New York, 1992, 3rd Volume
2. Wille, D; Holz, M: "Repetitorium der Linearen Algebra", Binomi Verlag, 1994