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Definition: Dimension of a Vector Space
The dimension \(\operatorname {dim}(V)\) of a vector space \(V\) is the maximum number \(n\) of linearly independent vectors contained in \(V\). If no such maximum number exists, we set \(dim(V)=\infty\).
- If \(\operatorname {dim}(V) = \infty\), \(V\) is called a infinitely dimensional vector space.
- If \(\operatorname {dim}(V) < \infty\), \(V\) is called a finitely dimensional vector space.
Mentioned in:
Definitions: 1 2 3 4 5 6 7 8
Proofs: 9 10
Theorems: 11
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References
Bibliography
- Wille, D; Holz, M: "Repetitorium der Linearen Algebra", Binomi Verlag, 1994
