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Theorem: Finite Basis Theorem

If \(V\) is a vector space over a field \(F\) with a finite dimension \(dim(V) < \infty\), then:

1. \(V\) has a finite basis.
2. Two different bases of \(V\) have the same number of elements, and this number equals \(n=dim(V)\).
3. Two different bases of \(V\) have the same number of elements, and this number equals \(n=dim(V)\).

Table of Contents

Proofs: 1

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References

Bibliography

1. Koecher Max: "Lineare Algebra und analytische Geometrie", Springer-Verlag Berlin Heidelberg New York, 1992, 3rd Volume