Basis

Definition: Basis

A basis of a vector space $(V,K,+,\cdot )$ is a linearly independent spanning set of $(V,K,+,\cdot )$.

Equivalent Definition

A set $B$ of vectors is a basis of a vector space $(V,F,+,\cdot )$ if and only if $B$ is a maximally linearly independent.

PROOF

TODO

Equivalent Definition

A set $B$ of vectors from is a basis of a vector space $(V,F,+,\cdot )$ if and only if $B$ is a minimal spanning set.

PROOF

TODO