Συζήτηση:Διανυσματικός χώρος

I'll post here in english for my written greek isn't good enough.

The chapter about bases has to be reworked. What exactly is the definition of smallest set of elements who generate the vector space? Furthermore, though it is in almost all cases true that a vector space contains more than one base it isn't generally true. The vector space {0} and the field with two elements are the only exceptions to the rule having exactly one base.

It would be better to introduce linear combinations and the notion of a generating set. Then define base as a generating set B that is minimal meaning that no proper subset of B generates the given vector space.

Finally, a more algebraic definition of vector space should be used. A K-vector space is an abelian group (V,+) with an action of a field K on V KxV->V such that...