Definition:Basis of Vector Space

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Let $K$ be a division ring.

Let $\struct {G, +_G, \circ}_R$ be a vector space over $K$.

Definition 1

A basis of $G$ is a linearly independent subset of $G$ which is a generator for $G$.

Definition 2

A basis is a maximal linearly independent subset of $G$.

Also known as

A basis of a vector space can also be referred to as a basis for a vector space.

A basis of a vector space over a subfield of $\C$ may also be known as a Hamel basis, to contrast with Schauder basis.

Also see

  • Results about bases of vector spaces can be found here.


Linguistic Note

The plural of basis is bases.

This is properly pronounced bay-seez, not bay-siz.